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3. Two equations about interior angles in n-gons are given here. a. Explain what each one calculates. (n-2)180° (n-2)180° n

3. Two equations about interior angles in n-gons are given here. a. Explain what each one calculates. (n-2)180° (n-2)180° n

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Topic: Interior Angles in n-gons** 3. Two equations about interior angles in \( n \)-gons are given here. **a. Explain what each one calculates.** 1. \((n - 2) \cdot 180^\circ\) 2. \(\frac{(n - 2) \cdot 180^\circ}{n}\) ### Explanation: 1. **Total Sum of Interior Angles:** The equation \((n - 2) \cdot 180^\circ\) calculates the **total sum of the interior angles** in an \( n \)-gon, where \( n \) represents the number of sides. This formula is derived from the fact that any \( n \)-gon can be divided into \((n - 2)\) triangles, and each triangle has an angle sum of \( 180^\circ \). 2. **Measure of Each Interior Angle in a Regular n-gon:** The equation \(\frac{(n - 2) \cdot 180^\circ}{n}\) calculates the **measure of each interior angle** in a regular \( n \)-gon (a polygon with all sides and angles equal). This is done by dividing the total sum of the interior angles by the number of angles, which is \( n \). These equations are essential for understanding the geometric properties of polygons and are widely used in various mathematical and practical applications.
Transcribed Image Text:**Topic: Interior Angles in n-gons** 3. Two equations about interior angles in \( n \)-gons are given here. **a. Explain what each one calculates.** 1. \((n - 2) \cdot 180^\circ\) 2. \(\frac{(n - 2) \cdot 180^\circ}{n}\) ### Explanation: 1. **Total Sum of Interior Angles:** The equation \((n - 2) \cdot 180^\circ\) calculates the **total sum of the interior angles** in an \( n \)-gon, where \( n \) represents the number of sides. This formula is derived from the fact that any \( n \)-gon can be divided into \((n - 2)\) triangles, and each triangle has an angle sum of \( 180^\circ \). 2. **Measure of Each Interior Angle in a Regular n-gon:** The equation \(\frac{(n - 2) \cdot 180^\circ}{n}\) calculates the **measure of each interior angle** in a regular \( n \)-gon (a polygon with all sides and angles equal). This is done by dividing the total sum of the interior angles by the number of angles, which is \( n \). These equations are essential for understanding the geometric properties of polygons and are widely used in various mathematical and practical applications.
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