8-1+Study+Guide


 * Lesson 8-1**

**ARCHITECTURE** **The Pentagon in Washington, D.C., Is shaped like a regular pentagon. Find the sum of the measures of the interior angles of the largest pentagon-shaped section of the Pentagon building.** Since the Pentagon is a convex polygon, we can
 * Example 1 Interior Angles of Regular Polygons**

use the Interior Angle Sum Theorem. //S// = 180(//n// - 2) Interior Angle Sum Theorem = 180(5 - 2) //n// = 5 = 180(3) or 540 Simplify.

The sum of the measures of the interior angles is 540.

Use the Interior Angle Sum Theorem to write an equation to solve for //n//, the number of sides. //S// = 180(//n// - 2) Interior Angle Sum Theorem (135)//n// = 180(//n// - 2) //S// = 135//n// 135//n// = 180//n// - 360 Distributive Property 360 = 45//n// Subtract 135//n// and add 360 to each side. 8 = //n// Divide each side by 45. The polygon has 8 sides.
 * Example 2 Sides of a Polygon**
 * The measure of an interior angle of a regular polygon is 135. Find the number of sides of the polygon.**

**ALGEBRA** **Find the measure of each interior angle.**
 * Example 3 Interior Angles**

Since //n// = 4, the sum of the measures of the interior angles is 180(4 – 2) or 360. Write an equation to express the sum of the measures of the interior angles of the polygon. 360 = //mR// + //mS// + //mT// + //mU// Sum of measures of angles 360 = //x// + 2//x// + 3//x// + 4//x// Substitution 360 = 10//x// Combine like terms. 36 = //x// Divide each side by 10. Use the value of //x// to find the measure of each angle. //mR// = 36, //mS// = 2 36 or 72, //mT// = 3 36 or 108, //mU// = 4 36 or 144.


 * Example 4 Exterior Angles**
 * Find the measures of an exterior angle and an interior**

At each vertex, extend a side to form one exterior angle. The sum of the measures of the exterior angles is 360. A convex regular nonagon has 9 congruent exterior angles. 9//n// = 360 //n// = measure of each exterior angle
 * angle of convex regular nonagon //ABCDEFGHI//.**