1. Chapter 6.1 Angles of Polygons

2. Concept 1

3. Find the Interior Angles Sum of a Polygon A. Find the sum of the measures of the interior angles of a convex nonagon. A nonagon has nine sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior angle measures. (n – 2) ● 180=(9 – 2) ● 180n = 9 =7 ● 180 or 1260Simplify. Answer:The sum of the measures is 1260.

4. A.900 B.1080 C.1260 D.1440 A. Find the sum of the measures of the interior angles of a convex octagon.

5. Find the Interior Angles Sum of a Polygon B. Find the measure of each interior angle of parallelogram RSTU.

6. A.x = 7.8 B.x = 22.2 C.x = 15 D.x = 10 B. Find the value of x.

7. Interior Angle Measure of Regular Polygon ARCHITECTURE A mall is designed so that five walkways meet at a food court that is in the shape of a regular pentagon. Find the measure of one of the interior angles of the pentagon.

8. A.130° B.128.57° C.140° D.125.5° A pottery mold makes bowls that are in the shape of a regular heptagon. Find the measure of one of the interior angles of the bowl.

9. Find Number of Sides Given Interior Angle Measure The measure of an interior angle of a regular polygon is 150. Find the number of sides in the polygon.

10. A.12 B.9 C.11 D.10 The measure of an interior angle of a regular polygon is 144. Find the number of sides in the polygon.

11. Concept 2

12. Find Exterior Angle Measures of a Polygon A. Find the value of x in the diagram.

13. Find Exterior Angle Measures of a Polygon B. Find the measure of each exterior angle of a regular decagon. A regular decagon has 10 congruent sides and 10 congruent angles. The exterior angles are also congruent, since angles supplementary to congruent angles are congruent. Let n = the measure of each exterior angle and write and solve an equation. 10n=360Polygon Exterior Angle Sum Theorem n=36Divide each side by 10. Answer:The measure of each exterior angle of a regular decagon is 36.

14. A.10 B.12 C.14 D.15 A. Find the value of x in the diagram.

15. A.72 B.60 C.45 D.90 B. Find the measure of each exterior angle of a regular pentagon.