Question

20. Find the measure of each interior angle AND each exterior angles of the following regular polygons. Show your work. a. Pentagon b. 16-gon c. Dodecagon

Answer 1

a. Pentagon

Interior angle:

5 sides => form 5 triangles => central angle: 360 / 5 = 72°

interior angle = 2x

angles in every triangle: x => x + x + 72° = 180°

=> 2x = 180° - 72° = 108°

Answer 108°

Exterior angles = 360° / number of sides = 360° / 5 = 72°

Answer: 72°

b. 16 - gon

Interior angles: 2x

number of triangles = 16

central angle = 360 / 16 = 22.5°

interior angle 2x, where 180° - 22.5° + x + x => 2x = 180° - 22.5° = 157.5°

Answer: interior angle 157.5°

Exterior angles: 360 / 16 = 22.5°

Answer: exterior angles = 22.5°

c. Dodecagon

number of sides 12

central angle = 360° / 12 = 30°

interior angle, 2x => 30 + 2x = 180 => 2x = 180 - 30 = 150°.

Answer: interior angle = 150°

Exterior angle = 360° / number of sides = 360° / 12 = 30°

Answer: exterior angle = 30°