15 sided polygon interior angles sum Since there are n vertices, there will be n linear pairs Learn more about how angles in an ๐-sided polygon add to 180° × (๐ – 2) with this BBC Bitesize Maths article. In real-world applications, this principle can be used in fields like architecture where knowing angle sums is crucial for designs involving polygons, such as a 15-sided building layout. A regular polygon with an interior angle of 162° has 20 sides. Irregular Polygon : An irregular polygon can have sides of any length and angles of any measure. Apr 28, 2022 ยท The method of finding the sum of the interior angles of a polygon is by multiplying the (number of sides)-2 by 180, so the sum of the interior angle measures in a 25-sided polygon would be 23*180, or 4140 degrees. Sum of Angles Formula We use the sum of angles formula to determine the sum of interior angles of a polygon. Apr 28, 2022 ยท How do you find angles of a parallelogram? To find the angles of a parallelogram, you have to know at least one angle (although it could be an interior or an exterior angle). The sum of the measures of the interior angles of a polygon is always 180 (n - 2) degrees, where n represents the number of sides of the polygon. Oct 18, 2017 ยท For a polygon with 15 sides (a 15-gon), we substitute n=15 into the formula: Therefore, the sum of the measures of the interior angles of a 15-sided polygon is 2340โ. Therefore, for a 24-sided polygon, each exterior angle would measure 360 degrees divided by 24, which equals 15 degrees. And we also have different types of polygons like triangles, quadrilaterals, pentagons, hexagons, etc, based on the number of sides of a polygon. That knowledge can be very useful when you're solving for a missing interior angle measurement. Find the sum of the interior angles of a pentagon, using the formula. • For triangles, n = 3, the sum is 180 โ. 9. How many sides does the polygon Feb 14, 2022 ยท For example, a triangle (3-sided polygon) has a sum of interior angles of 180 degrees, and a quadrilateral (4-sided polygon) has a sum of 360 degrees. Aug 2, 2019 ยท To find the measure of an interior angle in a regular 15-sided polygon, calculate the sum of interior angles using (n-2) x 180 and divide by 15, finding that each interior angle measures 156 degrees. What is the sum of the EXTERIOR angles of a pentagon? Nov 11, 2025 ยท Question 1: Regular polygon with each interior angle measuring 120° Let n be the number of sides. At each vertex of a polygon, there is both an interior and exterior angle, corresponding to the angles on the inside and outside of the closed figure. In a regular polygon, all interior angles are equal. At each vertex of the polygon, the interior angle and the exterior angle form a linear pair. , A polygon in which any of its diagonals contain points in the Jun 8, 2024 ยท Others Ways of Classifying Polygons 1) Based on Interior Angles a) Convex Polygon It is a polygon that has all its interior angles less than 180°. Oct 31, 2020 ยท Each interior angle of a regular 15-sided polygon measures 156°. Therefore, the formula for finding the angles of a regular polygon is given by; Sum of interior angles = 180° * (n – 2) Where n = the number of sides of a polygon. Mar 6, 2025 ยท To calculate the sum of the measures of the interior angles of a 15-sided polygon, also known as a pentadecagon, we can use a well-known formula: Thus, the sum of the interior angles of a 15-sided polygon is 2340โ . Check out this tutorial to learn how to find the sum of the interior angles of a polygon! The Sum of Exterior Angles Formula states that the sum of all exterior angles of any polygon is 360 degrees. Apr 28, 2022 ยท For a 15 sided polygon: interior_angle = (15 - 2) x 180o / 15 = 13 x 12o = 156o exterior_angle = 180o - interior_angle = 180o - 156o = 24o. Find step-by-step Geometry solutions and your answer to the following textbook question: Find the sum of the measures of the interior angles of the convex polygon: A 15-gon. Each angle in a regular polygon is equal to (n - 2) × 180° / n. Aug 13, 2025 ยท Interior angles of a polygon are angles within a polygon made by two sides. Mar 21, 2025 ยท $$ (5 – 2) \times 180^\circ = 540^\circ $$ Exterior Angles of a Polygon The exterior angles of a polygon are the angles formed between one side of the polygon and the extension of an adjacent side. Apr 28, 2022 ยท For a regular 15 sided polygon: exterior_angle = 360o / 15 = 24o interior_angle = 180o - exterior_angle = 180o - 24o = 156o Alternatively: The sum of the interior angles of a n-sided The sum of the interior angles of a polygon with n sides is given by the formula (n-2) * 180°. Calculate the interior and exterior angles of polygons using our polygon angle calculator. 2340 C. The interior angles in a regular polygon are always equal. There are some that wish to name every possible polygon, but there seems little point in doing so. The sum of the interior angles of a polygon is given by the formula: Aug 12, 2025 ยท Finding the interior angles of polygons is helpful for real life and solving geometric math problems. For example, we already covered the interior angle sum of any triangle = 180°. The sum of interior angles of polygon of 15 sides is : (n−2)×180o where n is the number of sides of polygon To find the interior angle sum of a polygon, we can use a formula: interior angle sum = (n - 2) x 180°, where n is the number of sides. (Don't type the word degrees into your answer, just put the value. When there is a polygon with four or more than four sides, we draw all the possible diagonals from one vertex. For example a 42-sided polygon is called a "tetracontakaidigon". Interior angle - An interior angle is an angle formed inside a polygon by two of its edges. The sum of the interior angles of a polygon is (n - 2) times 180, where n is the number of sides. Find the measure of each interior angle of a regular 15−gon. The sum of the measures of the interior angles of a polygon also depends on the number of sides. Feb 25, 2025 ยท Answer: Measure of each interior angle =2340o15=156o. Regular polygon has all sides equal in length and all angles equal in size. The sum of interior angles for any polygon is given by Question What is the sum of the interior angles of a 15 sided polygon? Select one: a. Apr 5, 2024 ยท LectureNotes said a regular polygon has 15 sides. so a 15 sided polygon has an angle sum of 2340. Here, n = 15 ∴ The sum of the interior angles of a polygon = ( 15 − 2 ) × 180 o . a. Understanding interior angles is essential in geometry, aiding in calculations for construction, design, and academic studies. And also, we can use this calculator to find sum of interior angles, measure of each interior angle and measure of each exterior angle of a regular polygon when its number of sides are given. A polygon is a plane shape (two-dimensional) with straight sides. G. There is your answer For example, 15-2 = 13 13 x 180 = 2340. The exterior angles of a regular hexagon measure 60°. (15-2) * 180 = 13 * 180 = 2340 degrees. Find the sum of the measures of the interior angles of a pentadecagon. 7. Since the 15-gon is regular, this total is shared equally among the 15 interior angles. A regular hexagon can be divided into 6 equilateral triangles. This page includes a lesson covering 'how to find the sum of the interior angles of a polygon' as well as a 15-question worksheet, which is printable, editable and sendable. Triangles, all convex quadrilaterals, regular pentagon, and regular hexagon are common examples of a convex polygon. Nov 15, 2019 ยท Since the polygon is regular, all sides and angles are equal, so each turn at each vertex is the same, and of size 360°15=24° degrees. 180° b. Apr 28, 2022 ยท The sum of the exterior angles of any polygon is always 360 degrees. Then, S = (2 x 15) - 4 = 26 right angles = 26 x 90 = 2340° So, each interior angle of a regular 15-sided polygon measures 2340/15 = 156° 2) Calculate the In order to find the measure of a single interior angle of a regular polygon (a polygon with sides of equal length and angles of equal measure) with n sides, we calculate the sum interior angles or $$ (\red n-2) \cdot 180 $$ and then divide that sum by the number of sides or $$ \red n$$. Each interior angle = $$\frac {2340^\circ} {15} = 156^\circ$$152340โ = 156โ Jul 23, 2025 ยท A regular polygon is a polygon whose all sides and all interior angles are measured the same, whereas an irregular polygon is a polygon whose all sides and all interior angles do not measure the same. Jun 14, 2023 ยท To find the measure of a single interior angle of a regular polygon, we simply divide the sum of the interior angles value with the total number of sides. A regular polygon has 15 sides. In geometry, a pentadecagon or pentakaidecagon or 15-gon is a fifteen-sided polygon. What is the size of an interior angle on a regular 15 sided shape? Or, Interior angle and exterior angle add to 180 degrees, so, each exterior angle is 360 degrees divided by 15 = 24 degrees. In this case, n = 15. Find the measure of each interior angle. = 13 × 180 o = 2340 o . Each triangle has an angle sum of 180 degrees, so the sum of the interior angles of the 15-gon must be 13 × 180 = 2340 degrees. By its formation, an exterior angle is supplementary to its adjacent interior angle. Students will first learn about interior angles of a polygon as part of geometry in high school. The sum of angles of a polygon is the total measure of all interior angles of a polygon. Understanding the Applying Standard 8. Therefore, to find the size of each interior angle, divide the sum of the interior angles by the number of sides. Jul 27, 2019 ยท Each triangle has an angle sum of 180 degrees, so the sum of the interior angles of the 15-gon must be (n-2) 13 × 180 = 2340 degrees. Examples include triangles, quadrilaterals Jan 17, 2025 ยท To find the sum of the interior angles of a polygon, we use the formula: S = (n−2)×180 where n is the number of sides of the polygon. And an exterior angle of a polygon is the angle between a side and its adjacent extended side. This is calculated by first determining the sum of all interior angles, which is 2340°, and then dividing that by the number of angles, which is 15. After examining, we can see that the number of triangles is two less than the number of sides, always. The measure of each exterior angle in a dodecagon (twelve-sided regular polygon) is 360 โ 12 = 30 โ. Step-by-step explanation: Still have questions? Jul 10, 2025 ยท Since the polygon is regular, all the interior angles are equal. E. . The interior angles of a polygon are equal to a number of sides. Oct 30, 2020 ยท Polygon In two-dimensional geometric figures, Polygon is a figure which has a finite number of sides and each sides will connected end to end. Students also learn the following formulas related to convex polygons. Find: a the sum of the interior angles bthe sum of the exterior angles e the size of each interior angle d the size of each exterior angle. The interior angle sum is the grand total of all those dishes. Mar 10, 2025 ยท A polygon is any closed figure with sides made from straight lines. For example the interior angles of a pentagon always add up to 540° no matter if it regular or irregular, convex or concave, or what size and shape it is. 6x = 570 Divide both sides by 6. Each exterior angle of a regular pentadecagon = 360/15 = 24 deg, so each interior angle is 180–24 = 156 deg. Jun 11, 2025 ยท Thus, the sum of the interior angles of a polygon with 15 sides is 2340โ. A regular hexagon is always convex. The formula for each interior angle of a regular polygon is: Interior angle= n(n−2)×180° Set this equal to 120°: n(n−2)×180 = 120 Multiply both sides by n: (n−2)×180= 120n 180n−360= 120n 60n= 360 n= 6 Answer: Hexagon (6 sides) Polygon definition and propertiesNamed Polygons Many polygons have names based on the number of sides. Jan 21, 2020 ยท Additionally, if we have a regular polygon (i. The sum of angles in a polygon depends on the number of vertices it has. For a 15-sided polygon, this results in a sum of 2340 degrees. You have already learned that the name of a polygon depends on the number of sides in the polygon: triangle, quadrilateral, pentagon, hexagon, and so forth. Angles are generally measured using degrees or radians. So, if a polygon has 4 sides, then it has four angles as well. An interior angles of polygon calculator is a tool to determine the sum of interior angles for a given polygon. Jun 6, 2025 ยท The interior angle sum of a polygon with 15 sides can be calculated using the formula (n - 2) × 180 degrees. The sum of interior angles of any polygon can be calculated using a formula. Polygon: Number of sides: n = Draw a line segment on the fi gure that divides it into two triangles. May 31, 2025 ยท The sum of interior angles in a polygon is calculated using the formula: Sum of Interior Angles = (n - 2) x 180°, where n is the number of sides. Where n is the number of sides of the polygon. e. Divide 360 by 12 to fi nd the measure of ° one of the 12 congruent exterior angles. Calculate the size of each interior angle. • For quadrilaterals, n = 4, the sum is 360 โ. There are several facts about all parallelograms:the sum of the interior angles is 360ห (true for all quadrilaterals)opposite angles are congruent (angles that are diagonal in parallelograms have the same measure Oct 27, 2014 ยท The Polygon Sum Formula states that for any n gon, the interior angles add up to (n 2) × 180 โ → n = 8 (8 2) × 180 โ 6 × 180 โ 1 080 โ Once you know the sum of the interior angles in a polygon it is easy to find the measure of ONE interior angle if the polygon is regular: all sides are congruent and all angles are congruent. Polygons are all around us, from doors and windows to stop signs. The interior angle sum of this polygon can now be found by multiplying the number of triangles by 180°. Step-by-step explanation: The sum of the interior angles of a polygon = ( n − 2 ) × 180 o . POLYGONS A polygon is a shape with straight sides that do not cross each other. A triangle has three sides. Sum - The sum is the total when numbers are added together. And, the sum of the interior angles of a regular pentadecagon is 15*156 = 2340 deg. Oct 28, 2018 ยท The polygon has 15 sides, calculated from the interior angle sum of 2340° using the formula for the sum of interior angles. Using the same formula, for a triangle: (3 − 2) × 180° = 180°, confirming that the sum of the interior angles for a triangle is 180°. Key Concepts Polygon: A closed figure with straight sides. Jan 30, 2025 ยท The sum of the interior angles of a 15-sided polygon is 2340°. A 5-sided polygon is called a pentagon for example. Learn how to calculate the sums of the interior angles here! Study with Quizlet and memorize flashcards containing terms like Use the Polygon Exterior Angle Sum Theorem to find the measure of each of the exterior angles of the regular pentagon. All the diagonals of a convex polygon lie inside the closed figure. Then the polygon is broken into several non-overlapping triangles. If a polygon does not cross over itself and has only one boundary, it is called a simple polygon. For a 15-sided polygon 1 Use the formula for the sum of interior angles of a polygon: Sum = (n-2) * 180 degrees, where n is the number of sides of the polygon Study with Quizlet and memorize flashcards containing terms like What is the measure of one angle of a regular hexagon?, What is the measure of one angle of a regular nonagon?, A regular pentagon and an irregular pentagon both have the same total interior angle measurement. Is there more than one way to do this? Explain. Nov 28, 2023 ยท The sum of the interior angles of a 15-sided polygon is calculated using the formula (n - 2) × 180°, which equals 2340°. Find the sum of the interior angles of a triangle, using the formula. 2. For a 15-sided polygon 1 Use the formula for the sum of interior angles of a polygon: Sum = (n-2) * 180 degrees, where n is the number of sides of the polygon Note: Polygons have all kinds of neat properties! For example, if you know the number of sides of a polygon, you can figure out the sum of the interior angles. Understand the sum of exterior angles formula using examples. For a 15-sided polygon: Sep 30, 2025 ยท Revision notes on Angles in Polygons for the Cambridge (CIE) IGCSE Maths syllabus, written by the Maths experts at Save My Exams. One important fact about the exterior angles of any polygon is that they always sum to $$360^\circ$$, regardless of the number of sides. The sum of interior angles of n sided polygon is s = (n - 2) x 180° Measure of each angle = (n - 2) × 180 n Dec 10, 2024 ยท An example of another polygon is a triangle, which has 3 sides. Beyond about 10 sides, most people call them an "n-gon". Here is what we know about exterior angles and polygons: 1. • All polygons can be divided into triangles, which helps derive the formula. We know that the sum of the exterior angles of a regular polygon is 360°. , The Polygon Interior Angle Sum Theorem states that the sum of the measures of the interior angles of a convex polygon with n sides is _____. The interior and exterior angles of a polygon are supplementary, that is sum to 180o. Nov 30, 2023 ยท The exterior angles of a regular polygon sum to 360 โ. 8. Oct 16, 2024 ยท To find the measure of each interior angle and each exterior angle of a regular polygon with 15 sides, you can follow these steps: Exterior Angles: For any polygon, the sum of all exterior angles is always 360 degrees. If the polygon is regular, we can calculate the measure of one of its interior angles by dividing the total sum by the number of sides of the polygon. Oct 26, 2022 ยท The value of h is 30. Imagine you’re at a polygon party, and each angle is a guest bringing a dish to share. Whether you’re dealing with a triangle, a pentagon, or a shape with 52 sides (you know, just for fun), this handy tool will help you find the total measure of all the internal angles in a few clicks. Since all the angles inside the polygons are the same. This remains true for non Apr 28, 2022 ยท What is the measure if each interior angle of a regular polygon with 15 sides? Two ways to calculate the required angle. The sum of the measures of the interior angle of any polygon is the number of sides minus 2 multiplied by 180. Partner Activity 3 The sum of the interior angles of any polygon is represented by: 180 (n 2). Explanation Calculate the sum of interior angles using the formula: (n-2) * 180 where n is the number of sides, n=15. The values in the table above assume a regular polygon as in the picture. You can go a step further and divide 2340 by 15 Jan 30, 2025 ยท The sum of the interior angles of a 15-sided polygon is 2340°. A polygon with 18 sides has an interior angle sum of 2880 degrees. Let us learn about the sum of angles Learn how to calculate the sum and measure of interior angles of any polygon easily, with stepwise formulas, solved problems, and downloadable worksheets. By solving the equation, we find that n = (2340/180) + 2 = 15. Sum of Interior Angles of a Polygon Students learn the definitions of vertices and diagonals of polygons. Irregular polygons – Polygons with sides of different lengths and angles of different sizes. For a 15-sided polygon, the sum is (15-2) * 180° = 13 * 180° = 2340°. 5 Work with a partner. The formula is derived considering that we can divide any polygon into triangles. 2,340° d. 2560 B. True or False and more. There are two types of polygons: Regular polygons – Polygons with equal sides and equal angles. Why is the formula for interior angles (n – 2) × 180? Because a polygon can be divided into (n – 2) triangles, and each triangle has 180 degrees. Upon investigating, it is found that the number of Problems Involving Interior Angles of a PolygonSolution : Number of sides = 7 Sum of interior angles of given polygon = (n - 2)180° = (7 - 2)180° = (5)180° = 900° 60° + x° + x° + x° + x° + 2x° + 90° = 720° 150 + 6x = 720 Subtract 150 from both sides. The formula for sum of interior angles in a regular polygon is given by Sum of angles = (2n-4)90° Where n = numbers of sides of polygon Number of sides in given polygon = 15 ⇒ Sum of the angles = (2 What is the Interior Angle Sum of a Polygon? The interior angle sum of a polygon is the total measure of all the interior angles combined. An Angle Sum of Polygons Calculator helps you calculate the total sum of the interior angles of a polygon. Scroll down the page for more examples and solutions on the interior angles of a polygon. The sum of the interior angles of a polygon can be calculated by subtracting 2 from the number of sides of the polygon and multiplying by 180°. Since this is a regular polygon (meaning all sides and angles are equal), each exterior angle can be found by dividing 360 degrees by the number of sides. The calculator given in this section can be used to know the name of a regular polygon for the given number of sides. Also, the sum of interior angles of different polygons is different. The sum of the interior angles of any polygon can be calculated using the formula: (n - 2)180° where variable n = the number of sides the polygon has. If the sum of the interior angles of a polygon is 20 right angles, find the number of sides the polygon has 3. Nov 9, 2023 ยท To find the measure of each interior angle of a regular polygon with 15 sides, you use the formula for calculating the sum of interior angles of a polygon, which is (n-2) × 180 degrees, where n is the number of sides. Find the sum of the interior angles of a 15-sided polygon, using the formula. Nov 21, 2023 ยท This lesson shows how to locate interior and exterior angles in a regular polygon, use formulas to calculate their individual values and their sums. Otherwise, it is a complex polygon. The interior angles of a regular hexagon measure 120°. 1, you found the sum of the measures of the interior angles of a quadrilateral by dividing the quadrilateral into two triangles When you begin with a polygon with four or more sides and draw all the diagonals possible from one vertex, the polygon then is divided into several nonoverlapping triangles. g. We will apply this formula for each of the given polygons. Can I use decimal values for sides? No, the number of sides must be a whole number (polygon sides cannot be in decimals). The sum of interior angles in a polygon can be calculated using the formula (n-2) * 180, where n is the number of sides For a 15-sided polygon, the total angle sum = (15-2) * 180 = 13 * 180 = 2340 degrees The size of each angle = total angle sum / number of sides = 2340 / 15 = 156 degrees Helpful Not Helpful Explain Simplify this solution Gauth The angle sum of this polygon for interior angles can be determined on multiplying the number of triangles by 180°. Mar 9, 2021 ยท A pentadecagon is a 15-sided polygon. Apr 28, 2022 ยท What is the Interior angle of a polygon with 15 sides? The interior angles of a 15 sided polygon add up to 2340 degrees and if it is a regular polygon then each interior angle is 156 degrees. To find the interior angle sum of a polygon, we can use a formula: interior angle sum = (n - 2) x 180°, where n is the number of sides. In a regular polygon, all sides are of same size and measure of all interior angles are the same. How to find the sum of interior angles of a polygon with 15 sides? Answer:A pentadecagon is a polygon with 15 sides. Jan 7, 2021 ยท The sum of the interior angle measures of any polygon can be calculated using the following expression (n is the number of sides the polygon has): 180(n −2) For a 15-sided polygon, plug in 15 for n and simplify: 180(15 − 2) = 180(13) Multiply to solve: 180(13) = 2340 For a 15-sided polygon, the sum of the interior angles must be 2340 degrees. 180 degrees – 24 degrees = 156 degrees. Find the size of an exterior angle of a regalar polygon with (a) 20 sides. In parts (a)−(e), identify each polygon and the number of sides n. Sep 28, 2020 ยท If the sum of the measures of the interior angles of a polygon is 2340°, how many sides does the polygon have? Use the equation “sum of interior angles = (n – 2)180º ” to write an equation and solve for n. Calculate the size of the exterior and interior angle in a regular pentagon . A polygon with n sides will have n interior angles and n exterior angles (one at each vertex). Therefore n = 3. 360° Show transcript Asked in United States Jun 15, 2022 ยท The sum of the interior angles in a polygon depends on the number of sides it has. What is the sum of interior angles of a hexagon? (6 – 2) × 180 = 720 degrees. 2 Given the radius ( r ) and height ( h ) of a cylinder, complete the flowchart below for calculating and disp Apr 28, 2022 ยท First off do X-2 then (X-2) x 180. For an irregular polygon, the unknown angle can be determined when measure of all other angles and their sum are known. The following diagram shows the formula for the sum of interior angles of an n-sided polygon and the size of an interior angle of a n-sided regular polygon. This is a KS2 lesson on finding the sum of the interior angles of a polygon. Properties of Polygon The important properties of the polygon are The sum of the interior angles of all the quadrangles = 360°. The following are some examples of regular and irregular polygons. In Lesson 6. To find one interior angle's measure, divide by the total number of angles, which is also the total number of sides. Mar 16, 2025 ยท To calculate the sum of interior angles, start by counting the number of sides in your polygon and plug this number into the formula for the "n" value. 2480 D. Sum of Interior Angles = (n − 2) × 180° In this article, we will learn about the interior angles of a polygon Apr 28, 2022 ยท The sum of the exterior angles of a polygon is 360o, so for a regular n-sided polygon, each is 360o/n. Divide the total sum by the number of sides: 2340 / 15 = 156 degrees. Jul 3, 2019 ยท Answer:A pentadecagon is a polygon with 15 sides. What is the Interior Angle Sum of a Polygon? The interior angle sum of a polygon is the total measure of all the interior angles combined. A pentadecagon is a polygon with 15 sides, and the sum of its interior angles is 2340 degrees. If at least one of the interior angles is > 180 degrees, then it is called a concave polygon. For a 15-sided polygon, we substitute n=15 into the formula: Therefore, the sum of the measures of the interior angles of a 15-sided polygon is 2340โ. Interior angles of a polygon Here you will learn about interior angles of a polygon, including how to calculate the sum of interior angles for a polygon, single interior angles, and how to use this knowledge to solve problems. Feb 7, 2025 ยท The Interior Angle Calculator helps determine the sum of interior angles for polygons of any number of sides. What is the interior and exterior angle of a 15-gon? Regular and Irregular Polygons Regular Polygon : A regular polygon has sides of equal length, and all its interior and exterior angles are of same measure. To find the measure of one interior angle, divide the total sum of the interior angles by the number of sides: 2340โ15=156โ\frac {2340^\circ} {15} = 156^\circ Therefore, each interior angle of a regular polygon with 15 sides is 156°. This tool simplifies the process of calculating angles, saving time and effort. What are interior angles? Interior angles are the angles inside a shape. b) Concave Polygon Also known as a non-convex polygon, it is a For example, a square has all its interior angles equal to the right angle or 90 degrees. 3. , all sides and angles are equal), then we can find the measure of each interior angle by dividing the sum of the interior angles by the number of sides. For example, a pentagon has 5 sides, so its interior angle sum is (5 - 2) x 180° = 3 x 180° = 540°. ⇒ Measure of each What is the sum of the interior angles of a 15-sided regular polygon? A. What is the sum of the angles of 15 sided polygon? Each triangle has an angle sum of 180 degrees, so the sum of the interior angles of the 15-gon must be 13 × 180 = 2340 degrees. The interior angles of any polygon always add up to a constant value, which depends only on the number of sides. In a regular polygon, all angles and sides are equal, which means that a perfect circle can be drawn across all the vertices. This is found by calculating the measure of one interior angle of the 25-sided polygon and equating it to (6h− 15)โ. ) Solution For (b) Calculate the sum of interior angles of a 15 sided polygon. Apr 28, 2022 ยท The interior angles of a 15 sided polygon add up to 2340 degrees and if it is a regular polygon then each interior angle is 156 degrees. Therefore, the measure of each angle is 156°. Helpful Not Helpful Explain Simplify this solution Gauth AI Pro Aug 12, 2025 ยท Finding the interior angles of polygons is helpful for real life and solving geometric math problems. 1. 2620 12 mins ago Discuss this question LIVE 12 mins ago One destination to cover all your homework and assignment needs Learn Practice Revision Succeed Instant 1:1 help, 24x7 60, 000+ Expert tutors Textbook solutions Big idea maths, McGraw-Hill Education etc Essay review Get expert feedback on your Keywords Polygon - A polygon is a flat (2D), closed figure made up of straight line segments. Each interior angle must have a measure of 2340 ÷ 15 = 156 degrees. Figure illustrates this division using a sevenโsided polygon. For example a 15-gon The sum of the interior angle measures of an n-sided convex polygon is (n - 2) times 180. Jan 14, 2020 ยท What do the exterior angles in a Pentagon add up to? Calculating the exterior angles of regular polygons Remember the interior and exterior angle add up to 180°. Show Step-by-step Solutions Apr 28, 2022 ยท 156 degrees Sum of interior angles of a polygon=180(n-2), where n is the number of sides. You can see how the formula applies to polygons with different numbers of sides. Jan 26, 2023 ยท Learn the Interior Angle Formula for polygons, apply the formula to find the sum of the interior angles of a polygon, and use it to find an unknown interior angle. What is the exterior angle of a 15 sided polygon? The exterior angles of a REGULAR 15-gon are 204o, so the sum would be 3060o. Learn how to calculate the sums of the interior angles here! May 22, 2019 ยท To find the sum of the measures of the interior angles of a polygon, we can use the formula: where n is the number of sides of the polygon. • The formula for the sum of interior angles depends on the number of sides n. Step 2: Calculate the size of each interior angle Each interior angle of a regular polygon is the sum of the interior angles divided by the number of sides. Each interior angle of a regular 15-sided polygon measures 156°. For students between the ages of 11 and 14. By the Polygon Exterior Angles Theorem, the sum of the measures of the exterior angles, one angle at each vertex, is 360 °. x = 95 Problem 6 : A regular polygon has interior angle of 156°. Each polygon has a different number of sides, and this calculator helps to find the sum of its interior angles. Answer: To find the measure of each interior angle of a regular polygon with 15 sides, we can use the formula: Interior Angle = (n-2) x 180° / n where n is the number of sides of the polygon. • This theorem applies only to convex polygons. Then fi nd the sum of the interior angle measures of the polygon. 1) Use the formula S = 2n - 4 right angles S is the sum of the interior angles of a polygon, n is the number of sides. Examples Angles of a Triangle: The sides and interior angles of a regular hexagon are all equal. They are the angles within a polygon made by two sides: Interior and exterior angles form a straight line – they add to 180°: We can calculate the sum of the interior angles of a polygon by splitting it into triangles and multiplying the number of triangles by 180°. The sum of the interior angles of a regular hexagon is 720°. The Polygon Sum Formula states that for any n−gon, the interior angles add up to (n 2) × 180 โ. 3,280° C. pze ytznw cmxm cmv ptkiy loxpm xzrxsr tmjtf jiofwgcz bqiryl ipowx ufjiq fnaklrz ruxscu gxmq