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Math Geometry Practice | Interior and Exterior Angles of Polygons

Warm up your thinker by solving homework questions on interior and exterior angles of polygons. Practice with regular shapes, sums of angles, and exterior angle measures. Get ready for math success!

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Math Geometry Practice | Interior and Exterior Angles of Polygons

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  1. Warm up the ol’ thinker Get out your homework! Solve for x:

  2. HOMEWORK QUESTIONS? • Pg 300 1-15

  3. Ex. 1 Use the regular pentagon to answer the questions. • Find the sum of the measures of the interior angles. • Find the measure of ONE interior angle 540° 108°

  4. Ex. 2 Use a regular 15-gon to answer the questions. • Find the sum of the measures of the interior angles. • Find the measure of ONE interior angle 2340° 156°

  5. Find the measures of one interior angle of the indicated polygon. • Regular triangle • Regular heptagon • Regular dodecagon

  6. What about the outside? Finding and using the exterior angle measures of polygons

  7. 2 1 3 5 4 In any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°.

  8. In any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. 1 3 2

  9. In any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. 1 2 4 3

  10. Ex. 1 Find the measure of ONE exterior angle of a regular hexagon. 60°

  11. Ex. 2 Find the measure of ONE exterior angle of a regular heptagon. 51.4°

  12. Ex. 3 Each exterior angle of a polygon is 18. How many sides does it have? n = 20

  13. Find the measures of an interior angle and exterior angle of the indicated polygon. • Regular triangle • Regular 20-gon • Regular nonagon • Regular heptagon • Regular dodecagon • Regular 17-gon

  14. How many sides does the polygon have? • Each interior angle has a measure of 140º • Each interior angle has a measure of 175.2º • Each exterior angle has a measure of 45º • Each exterior angle has a measure of 3º

  15. Ex: 3 The measure of each interior angle is 150°, how many sides does the regular polygon have? One interior angle A regular dodecagon

  16. Find the value of x: 142o 140o 105o 124o 88o xo

  17. Find the value of x: 64o 2xo 3xo 86o 110o

  18. Find the value of x: 60o 8xo 100o 6xo 20o 6xo

  19. The measures of the interior angles of a convex octagon are 45x, 40x, 155, 120, 155, 38x, 158, 41x. What is the measure of the smallest interior angle?

  20. Homework: Pg 301 # 26 - 35

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