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Chapter 6.1

Chapter 6.1. Angles of Polygons. Concept 1. 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.

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Chapter 6.1

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  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) ● 180 n = 9 = 7 ● 180 or 1260 Simplify. Answer: The sum of the measures is 1260.

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

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

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

  7. Interior Angle Measure of Regular Polygon ARCHITECTUREA 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 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. A. 130° B. 128.57° C. 140° D. 125.5°

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

  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 = 360 Polygon Exterior Angle Sum Theorem n = 36 Divide each side by 10. Answer: The measure of each exterior angle of a regular decagon is 36.

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

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

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