The sum of the angle measures of a polygon with n sides is 1080 find n. The sum of a polygon's interior angle measures is. Step 3 3 of 5 Jun 12, 2016 · Consider a triangle, a polygon with three sides. We are given that the sum of the interior angle measures is 1800°, so we can set up the equation { (n - 2) * 180} = 1800 and solve for n. We are given that the sum of the interior angles is 1800 degrees. Example 2: Using the angle sum formula verify that sum of interior angles of a triangle is 180 degrees. A polygon in which all sides are equal in length and all angles have the same measure is called regular. The sum of the measures of the angles of a polygon with n n sides is 1080. Find step-by-step Algebra solutions and your answer to the following textbook question: The sum of the interior angle measures of a polygon with n sides is given. 6 sides, 4 triangles, and 720 degrees. Jan 1, 2017 · As we know that sum of the interior angles of a triangle is 180∘, the sum of 8 interior angles of octagon will be 6 × 180∘ = 1080∘. Sum of interior angles = 540°. n-2=5. That means that all of these angles in the center add up to 360 degrees, and so, if we subtract 360, we'll be left with just the angles at the edges. That means that our sum will be n*180 - 360 = n*180 - 2*180 = (n-2)*180 May 1, 2016 · $\begingroup$ @nyorkr23 Let's say you do know that the sum of the angles on a triangle is $180^o$. The sum of the interior angles measures #360˚#. of sides . Explanation: To find the number of sides (n) of a polygon, we can use the formula: Sum = (n-2)180. Below is the proof for the polygon interior angle sum theorem. Sum of interior angles of a hexagon = (6 - 2) × 180° = 720° Thus, the sum of the interior angles of a hexagon is 720°. Interior Angle = Sum of the interior angles of a polygon / n. Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on. and for a rectangle, it is (4 − 2) × 180∘ = 2 × 180∘ = 360∘. Sum of interior angles of a polygon. angles of polygon with n sides ____ 4. Thus, the sum of the angles of any polygon is: S = ( n – 2) * 180. 1) 180^o \\2) 1080^o \\3) 1980^o \\4) 2880^o; What is the sum of the angle measures of a polygon with 37 sides? The sum of the angle measures of a polygon with n sides is 2340 . 6 ( 60 ∘ ) = 360 ∘ . Extension. angles of a polygon with 8 sides _____ 5. Adding 2 to both sides, we get: n = 12. For example, we use n = 5 n = 5 for a pentagon. The sum of the angle measures of a polygon with n sides is 1260. Put, sum of interior angles = 1080° (Given) 1080° = 180 (p – 2). Here’s the best way to solve it. Thus, we need to find: 1800 = 180 (n - 2) 10 = n - 2. find the number of sides of the polygon Find the sum of the interior angle measures of a convex octagon (an eight-sided polygon). The formula for the sum of interior angles, of a regular polygon with p sides is, Sum = 180 (p – 2). S u m = 1,080 °. Hence, the number of sides of the polygon is 8. The sum of the measures of the inferior angles in any polygon can be May 14, 2024 · So, the sum of interior angles of the polygon = n × 180° – 360°. As, the sum of the interior angles. For example for a triangle, it is (3 − 2) × 180∘ = 180∘. The Formula Given sum S S S, of the angles of a polygon with n sides is given by the formula. Therefore, the shape is a dodecagon, and the number of sides it has is 12. Aug 11, 2023 · A regular polygon is a polygon with all sides and angles equal. We can find the sum of interior angles of any polygon using the following formula: ( n − 2) × 1 8 0. O 51. Expert Answer. Feb 24, 2012 · The sum of the interior angles in a polygon depends on the number of sides it has. You can put this solution on YOUR website! The sum of the angle measures of a polygon with n sides is 1080. Step 3 3 of 5 Aug 31, 2019 · Click here 👆 to get an answer to your question ️ The sum of the interior angles of a polygon with n sides is Select one: a. The formula for calculating the sum of interior angles of a polygon is; S = ( n − 2 ) × 180° Find the sum of the measures of the angles of a nine-sided polygon. So we can set up the equation 1800 = 180 (n-2). what is a polygon called if the sim of its interior angles equals 6840? 4. 5. Step 1. Hence sum of the measures of the interior angles of a 21 sided polygon is (21 −2) × 180∘ = 19× 180∘ The sum of the interior angles in a regular polygon is given by the formula 180 ( n – 2), where n is the number of sides in the polygon. n = 10. Solution: Here, n = 7. Exterior angle: 18 exterior angles so 18x = 360, or x = 20. Solution A. Using the formula (n − 2) × 180 ° (n - 2) \times 180\text{\textdegree} (n − 2) × 180 °, where n n n is the number of sides, the sum of the angles of a 10-sided polygon can be determined. (n - 2) = 1440° / 180°. Explain why this formula works. its interior angles add up to 3 × 180° = 540° And when it is regular (all angles the same), then each angle is 540° / 5 = 108° (Exercise: make sure each triangle here adds up to 180°, and check that the pentagon's interior angles add up to 540°) Jun 7, 2019 · To solve for the number of sides n in a polygon given the sum of the interior angles, we use the formula: S = (n - 2) × 180° where S is the sum of the interior angles in degrees. 126 0 ∘. area = n × a² × cot(π/n)/ 4. Thus the number of sides of the polygon is 8. 7. We have shown that the three angles in a triangle have a sum of 180º. n = [?] A: For any regular polygon of sides n, measure of interior angle can be given by θ=(n-2)·180°n, where… Q: Find the length of the third side. Dec 29, 2020 · In this lesson we’ll look at how to find the measures of the interior angles of polygons. The sum of the angle measures of a polygon with n sides is 1080, then. 360 c. By its formation, an exterior angle is supplementary to its adjacent interior angle. 1 Lesson Finding the Sum of Angle Measures in a Polygon Find the sum of the measures of the interior angles of the fi gure. Exterior Angle an angle formed by one side of a polygon an the extension of an adjacent side. Oct 24, 2019 · Answer: 8. A polygon is a closed plane figure with three or more straight sides called edges. So, a polygon whose angles sum to 1800 degrees must have 12 sides. For example, a polygon with N = 22 sides has 180 (22 – 2) = 180 (20) = 3600 degrees. A polygon is regular if all of its edges are the same length and all of its angles have the same measure. 2 3. Answered 2 years ago. sum of all interior angles=(n-2)*180° Now, As given the sum of all angles=900° then number of sides of a polygon will be (n-2)*180=900. Therefore, a polygon with the sum of its interior angles Our expert help has broken down your problem into an easy-to-learn solution you can count on. The sum S of the measures of the interior angles of a polygon with n sides can be found using the formula S = 180(n − 2). Question. Therefore, the sum of the interior angles of a polygon is 900°. May 29, 2017 · Explanation: Sum of the measures of the interior angles of a polygon of n sides is (n −2) ×180∘. The sum of the angle measures of a polygon is 1080 . Question: Find the sum of the measures of the interior angles (in degrees) of a polygon of n sides for the following values of n. For example, the sum of all eight angles of an octagon is: S = (8 – 2) * 180 = 1080°. 2 EXPLORATION: Writing a Multi-Step Equation As a result, we may argue that all polygons are 2d forms, but not all two-dimensional figures are polygons. Solved examples on finding the sum of the interior angles of an n-sided polygon: 1. n=7. Interior Angles Theorem. The polygon angle-sum theorem states that the interior angles of a polygon all add up to 180 ⋅ (n − 2) 180\cdot(n-2) 180 ⋅ (n − 2) where n n n represents the number of sides. . The interior angles in a regular polygon are always equal. It has 8 sides. Verified. Learn more about polygon here: Use the polygon sum theorem to find the total measure of the interior angles, ten solve an algebraic equation to find the unknown angle. The Sum of interior angles of a octagon = (8-2) × 180°. It is a polygon that has n sides and n corners. Let's see the solution step by step. The sum of the interior angle measures is #180˚#. = (2 × 7 - 4) × 90°. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 The interior angles of a polygon are the angles formed inside a polygon by two adjacent sides. Mar 26, 2016 · 165^circ Always remember the formula (very important in geometry) Let the number of sides of a polygon (convex) =n Then the sum of measures of angles =color(blue)((n-2)*180 :. Solution B. = (n − 2) × 180 ° Use the formula = (10 − 2) × 180 ° Substitute the value of n = 8 × 180 ° Perform operation inside the parentheses = 1, 440 There are 180 (N – 2) degrees in a polygon if we add up the measures of every interior angle: Sum of Interior Angles of an N-gon = 180 (N – 2) degrees. So, (n -2) 180 = 1260. 8 sides, 6 triangles, and 1080 degrees. We’ll name polygons based on the number of sides, and then talk about the number of triangles that make up the polygon, and how to find the measure of each interior angle. Because the octagon is regular, all of its sides and angles are congruent. There are 2 steps to solve this one. = 540°. Transform the formula to find the number of sides in terms of the interior angle sum. Q: 3. How many sides does the polygon have? 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 anglesor $$ (\red n-2) \cdot 180 $$ and then divide that sum by the number of sides or $$ \red n$$. 1080. Nov 21, 2023 · Dividing the formula by n, one can find the value of each angle by: {eq}Angle = \frac { (n-2) * 180^\circ} {n} {/eq} Example 1: The items a to e that follow show the number of sides of a regular Answer: It is a regular octagon. Justify the steps in your solution. 3. Classify the polygon by the number of sides. 1980. Find the sum of the interior angle measures of a convex 18-gon (an eighteen-sided polygon). Algebra. Find the sum of the interior angles of a polygon of seven sides. (n-2)\times 180 (n − 2) × 180 °. Find the sum of the interior angle measures of the green polygon. = (3) × 180°. Final answer. If the measure of each interior angle of a regular polygon is 108, find the measure of each…. An octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 Q: If you know the total angle measure of a polygon, how would you find the number of sides the polygon… A: Simply use the formula for the total sum of internal angles of a n sides polygon. May 21, 2018 · 180(n-2) = 1080 180n - 360 = 1080 180n = 1080 + 360 180n = 1440 n = 1440/180 n = 8 The answer is 8 sides. A polygon with n sides will have n interior angles and n exterior angles (one at each vertex). To find the sum of the interior angles of a polygon, multiply the number of triangles in the polygon by 180°. Big Ideas Math Integrated Mathematics II. Step 3 3 of 4 To determine what the sum of the measures of the angles is, know how many sides the given polygon has. what is the sum of the interior angles of a pentagon? 2. Oct 22, 2017 · The sum of the angle measures of a polygon with n sides is 1440. Angle sum formula = ( n − 2) × 180°. Nov 10, 2023 · The polygon has 8 sides. 4 sides, 2 triangles, 360 degrees. n = [?] Q: If you know the total angle measure of a polygon, how would you find the number of sides the polygon… A: Simply use the formula for the total sum of internal angles of a n sides polygon. n = 7. Geometry. n = 8 + 2. Given that the sum of the interior angles S is 2280 degrees, we can set up the equation: 2280 = (n - 2) × 180. Mar 16, 2020 · The number of sides of the polygon is 18. Q: One of the acute angles in a right triangle has a measure of 35°. Step 3 3 of 4 Find step-by-step Geometry solutions and your answer to the following textbook question: The sum of the interior angle measures of a polygon with n sides is given. View the full answer. 5 sides, 3 triangles, 540 degrees. Question: If the sum of the interior angle measures of a polygon with n sides is 1980°, find n. For a hexagon, n = 6. If you want to calculate the regular polygon parameters directly from equations, all you need to know is the polygon shape and its side length: 1. Statement: In a polygon of ‘n’ sides, the sum of the interior angles is equal to (2n – 4) × 90°. Also, the measure of each exterior angle of an equiangular polygon = 360°/n. Therefore, the May 17, 2024 · Regular polygon formulas: sides, area, perimeter, angles. Then find the angle measures of each given polygon. What is a polygon? A polygon is simply a two-dimensional a plane shape enclosed by line segments called sides. Each exterior angle of a regular polygon of 10 sides _____ The polygon angle-sum theorem states that the interior angles of a polygon all add up to 180 ⋅ (n − 2) 180\cdot(n-2) 180 ⋅ (n − 2) where n n n represents the number of sides. 1) 180^o \\2) 1080^o \\3) 1980^o \\4) 2880^o; Find the sum of the measures of the interior angles and the sum of the exterior angles of a seventeen-sided convex polygon. (a) n = 7 900 (b) n=9. n = [?] Hint: Sum = (n-2)180. An endpoint of an edge a vertex. Step-by-step explanation: The formula to calculate the sum of interior angles of polygon is (n - 2)180. Write and solve an equation to find each value of x. This formula works whether or not the polygon is regular and even works if the polygon is convex. Explanation: To find the number of sides in a polygon given the sum of the interior angle measures, we can use the formula: Sum of Interior Angle Measures = (n - 2) * 180° Where 'n' represents the number of sides in the polygon. The sum of the interior angle of n side polygon is (n-2)×180° According to the problem, (n-2)×180° = 2880° or, n-2 = or, n-2 = 16. How many sides does the polygon have? Mar 20, 2024 · Last Updated : 20 Mar, 2024. Dec 28, 2022 · The sum of the angle measures of a polygon with n sides is 1080. Only using this, try to prove that the sum of the angles of a square is $360^o$. Find step-by-step Geometry solutions and your answer to the following textbook question: The sum of the interior angle measures of a polygon with n sides is given. (x - 2) x 180 where x is number of sides. Hence, For sum of all angles of polygon=900°, no Find the sum of the angle measures of the quadrilateral polygon. Given that the sum of the interior angle measures of the polygon is 1980°, we can substitute this value into the formula: 1980 = (n-2)180 Math. Divide both sides of the equation by 180: 2280 ÷ 180 Nov 3, 2023 · Explanation: A polygon is a closed shape with straight sides. Where “n” is the number of polygon sides. Once you know the sum of the interior angles in a polygon it is easy to find the measure of ONE 1 / 4. 2° 10° 3° 360° Oct 20, 2020 · For a polygon to have an interior angle sum of 1080°, number of its sides will be 8. 4° О 72° 120°. where n is the number of sides of the polygon. Solve this equation for n. n - 2 = 6. Therefore, S = 180n – 180 (n-2) S = 180n – 180n + 360. Sum of int. 1st Edition • ISBN: 9781680330687 Boswell, Larson. Formula. Answer: The sum of the interior angles of a regular pentagon is 540°. Sum of interior angles of polygon with 4 sides _____ 2. 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°. If the sum of the interior angle measures of a polygon with n sides is 1980°, find n. if the sum of the interior angles of a polygon equals 1080, then determine the sides of the polygon. A pentagon has 5 sides. The sum of the measures of the interior angles of a convex polygon is given. Find step-by-step Algebra solutions and your answer to the following textbook question: The sum of the angle measures of a polygon is $1080^ {\circ}$. All the interior angles in a regular polygon are equal. To find the number of the sides of the polygon we use the theorem of the sum of the interior angles: S n = ( n − 2 ) ⋅ 180 S_n=(n-2)\cdot180 S n = ( n − 2 ) ⋅ 180 Step 3 Given that the sum of the interior angles is 900°, we can set up the equation and solve for n: 900° = (n - 2) × 180° To solve for n, we first divide both sides of the equation by 180°: 900° / 180° = (n - 2) 5 = n - 2. The sum of the internal angle is 180 ( n - 2) degrees. 180 (n-2) = 1080. 360° 1080° Sum of interior angles: 9 Sides In Exploration 1, you were given the formula for the sum S of the angle measures of a polygon with n sides. Solution: To verify the sum of interior angles of a triangle is 180 degrees. (n - 2) = 8. 4,553 solutions. Then the number of sides of the polygon is given as, (n - 2) × 180° = 1440°. If necessary, round to the nearest tenth. 2° 10° 3° 360° Terms in this set (17) 3 sides, 1 triangle, and 180 degrees. Q: The sum of the interior angle measures of a polygon is 3,420°. angles of polygon with 8 sides. Our expert help has broken down your problem into an easy-to-learn solution you can count on. or, n = 18. The Lesson: A polygon with the fewest number of sides is a triangle. Substitute the number of sides into the formula. Thus, each interior angle of a regular heptagon = 900/7 = 128. _____ 3. In this case, we plug in the given value: 1080° = (n - 2) * 180° Simplifying the equation Mar 6, 2020 · the sum of the measures of the interior angles of a convex polygon is eight times the sum of the measures of its exterior angles. Then, use the polygon angle-sum theorem which states that an n n n -gon has angles that add up to ( n − 2 ) 180 (n-2)180 ( n − 2 ) 180 . 1080°. In our example, n = 5. We can therefore deduce that for each polygon with an additional side has #180˚# more than the previous figure. 2. The sum of the measures of the angles of a polygon with n sides is given. Each triangle has a sum of 180°. n- 2 = 6. 180(n-2) Using the formula (n − 2) × 180 ° (n - 2) \times 180\text{\textdegree} (n − 2) × 180 °, where n n n is the number of sides, the sum of the angles of a 10-sided polygon can be determined. Sum of the interior angles = (2n – 4) × 90°. The formula to calculate the sum of the interior angles of a polygon is (n - 2) * 180°, where n is the number of sides of the polygon. = (n −2) ×180∘. Area. Interior angles of a polygon are angles within a polygon made by two sides. Q: Find the measure of one interior angle of this regular polygon. A closed figure formed by 3 or more line segments called sides. The measure of each interior angle of a regular polygon = ( (n – 2) × 180°/n) (Since the measure of each angle is the same for a regular polygon) Hence proved. 180 b. The Polygon Sum Formula states that for any n − gon, the interior angles add up to ( n − 2) × 180 ∘. Answer: It is a regular octagon. Option A) polygon has 8 sides is the correct answer. Interior angle: There are 18 angles so 18x = 2800 or x = 160. Start with the formula: Sum of interior angles = (n − 2) × 180°. 6 13 Nov 13, 2017 · Because all of these triangles meet at the center, we can draw a full circle out of the angles where they meet. Apr 25, 2023 · The sum of the interior angles of a polygon with n sides is given by: Sum = (n - 2) * 180. Q: The sum of the exterior angles of a polygon is: 90° O 360° 720° 180°. Thus, by substituting in the above formula we get. Consider any quadrilateral, a polygon with four sides. arrow right. Sum of interior angles: 4 Sides. In this case, we have a regular polygon with 5 sides, so the sum of the interior angles can be calculated as: sum = (5 - 2) * 180 Oct 29, 2023 · By using the formula (n-2)180, the number of sides (n) can be determined as 13. S = 360°. = 900°. \newline Given S S S =1080 Math. Given, number of sides of the polygon be n. hello quizlet Find the measure of angles. Apr 23, 2020 · (sum of interior angles = 10 (n-2) where n is the number of sides of the polygon) 1. Thus, for a heptagon, n = 7. Hence, A pentagon has 5 sides, and can be made from three triangles, so you know what . Solution. Sum of Interior Angles = (n − 2) × Find the measures of an interior angle and an exterior angle of a regular 18-gon. 1 +0 Answers #1 +26379 0 . polygon with n sides into (n − 2) triangles shows that the sum of the measures of the interior angles of a polygon is a multiple of 180°. → n = 8 ( 8 − 2) × 180 ∘ 6 × 180 ∘ 1 080 ∘. Where n - number of sides, a - side length. Now, given sum of interior angle is. 180 (n-2) = Total angle. We use this fact to analyze polygons with more than three sides. Setting these two expressions equal to each other, we get: (n - 2) * 180 = 1800. Thus, the sum of interior angles of the polygon = (n – 2) × 180°. ° How many sides does the polygon have? Explain how you found your answer. The sum of the interior angle measures is 540°. Find n n. 1260^\circ. The Red Cross symbol is a convex 12-gon. Step-by-step explanation: Given, The sum of interior angles of a polygon is 2880° To find the number of sides of the polygon. An octagon has eight sides, so the sum of the angles of the octagon is 180 (8 – 2) = 180 (6) = 1080 degrees. Example Calculate the sum of the interior angles in a pentagon. If you then add 2 to both sides, you find that n = 12. S = ( 5 − 2) × 180°. Since an octagon has 8 sides, So put n = 8. Oct 22, 2017 · The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. SOLUTION The fi gure is a convex octagon. Sum of interior angles = (5 − 2) × 180°. = 6 × 180° = 1080°. Explanation: We have to solve this for a number of sides of the polygon (p). Feb 15, 2016 · Here, The Sum of interior angles of a polygon with n sides is given as, = (n-2) × 180°. May 26, 2022 · Polygon. Find step-by-step Algebra solutions and your answer to the following textbook question: To find S, the sum of the measures of the interior angles of a polygon with n sides, you can use the formula S = (n - 2)180. What is the sum of the angle measures of a polygon with 37 sides? Now, an important point is that the sum of the exterior angles of a regular polygon with n Figure 10. = (n − 2) × 180 ° Use the formula = (10 − 2) × 180 ° Substitute the value of n = 8 × 180 ° Perform operation inside the parentheses = 1, 440 For any polygon, the sum of the measures of the exterior angles is ALWAYS ___. The sum of the internal angle is 180(n-2) degrees. n; Question: The sum of the angle measures of a polygon with n sides is 2340 . Polygons each have a special name based on the number of sides they have. Now, let's add 2 to both sides to find n: n = 5 + 2. The sum of interior angles of a regular polygon is given using the interior angle formula that is (n - 2) × 180º where n is the number of sides of the polygon. Q: Determine the measure of one exterior angle of a regular 120-sided polygon. In your question, you know that the sum of the angles is 1800 degrees. 1. Sum of interior angles = 3 × 180°. Dividing both sides by 180, we get: n - 2 = 10. To solve this equation for 'n', you want to first divide both sides by 180 which gives you 10 = n - 2. Interior Angle Measures of a Polygon The sum S of the interior angle measures of a polygon with n sides is S = (n − 2) ⋅ 180°. Also, read: It is a polygon that has n sides and n corners. The sum of the angle measures of a polygon with n sides can be found using the formula S = 180 (n -2). The number of sides of the polygon that has a sum of the angles 1440° will be 10. The sum of the interior angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. = (n – 2) × 180°. For a polygon with n no. Thus, the requried sum of the interior angle measures of a regular octagon is 1080°. 1080° / 180 = (p – 2). Exercises 7– 9 Reading For polygons whose names you have not learned, you can use the Interior angle sum formula: Sum of interior angles of a Polygon = (n - 2) × 180° where n = number of sides. This formula works regardless of whether the polygon is regular or irregular. Comparing with this situation we can say that a polygon of n-sides can be divided into n −2 triangles and thereby the sum of the interior angles of polygon of n-sides will be. 57º The polygon angle-sum theorem states that the interior angles of a polygon all add up to 180 ⋅ (n − 2) 180\cdot(n-2) 180 ⋅ (n − 2) where n n n represents the number of sides. \newline n n n → \rightarrow → number of sides of a polygon. ----sum = (n-2)180 1080 = (n-2)180 n-2 = 6 n = 8 sides Proof: For any closed structure, formed by sides and vertex, the sum of the exterior angles is always equal to the sum of linear pairs and sum of interior angles. Q: If you know the total angle measure of a polygon, how would you find the number of sides the polygon… A: Simply use the formula for the total sum of internal angles of a n sides polygon. . n = 8. This forms an arithmetic series. To prove: Polygon Interior Angles Sum Theorem The sum of the measures of the interior angles of a convex polygon with n sides is ( n − 2 ) 180 ° . n = 12. At each vertex of the polygon, the interior angle and the exterior angle form a linear pair. The formula to find the sum of the interior angles of a regular polygon is given by: sum = (n - 2) * 180. Thus, the sum of the exterior angles is 6 ( 60 ∘ ) = 360 ∘ . That is, the sum of all interior angles in a 22-sided polygon is 3600 degrees. Related questions. Angle-sum is (18 – 2)180 = 16*180 = 2880. Here is what we know about exterior angles and polygons: 1. It is a regular polygon so all angles have equal measure. Sum of interior angles of a regular heptagon = (7 - 2) × 180º = 900º. n Dec 6, 2016 · The sum of the angle measures of a polygon with n sides is 1260. 2 3 5 2. Find n. Here, the angle sum for n side is 1260. More about the polygon link is given below. \newline S = 180 (n − 2) S = 180(n-2) S = 180 (n − 2), \newline where, \newline S S S → \rightarrow → sum of angles of a polygon. Where n represents number of sides The polygon angle-sum theorem states that the interior angles of a polygon all add up to 180 ⋅ (n − 2) 180\cdot(n-2) 180 ⋅ (n − 2) where n n n represents the number of sides. 1 / 4. 93, we multiply the measure of each exterior angle, 60 ∘ 60 ∘, by the number of sides, six. Solutions. Apr 19, 2017 · The summation of the angle measures of a polygon is given by: 180 (n - 2). oj jz vt ys qr zb eh pc oo jj