Question
Find the number of side of regular polygon whose each
Interior angle is a measure of 162°
Interior angle is a measure of 162°
Answers
Monica
Please answer this question
Bosnian
Sum of all the interior angles of any convex polygon of n sides is:
( 2 n - 4 ) ∙ 90°
Alsoo sum of n angles is n ∙ 162°
( 2 n - 4 ) ∙ 90° = n ∙ 162°
180° ∙ n - 360° = n ∙ 162°
Subtract n ∙ 162° to both sides
180° ∙ n - 162° ∙ n° - 360° = 0
18° ∙ n - 360° = 0
Add 360° to both sides
18° ∙ n = 360°
n = 360° / 18°
n = 20
( 2 n - 4 ) ∙ 90°
Alsoo sum of n angles is n ∙ 162°
( 2 n - 4 ) ∙ 90° = n ∙ 162°
180° ∙ n - 360° = n ∙ 162°
Subtract n ∙ 162° to both sides
180° ∙ n - 162° ∙ n° - 360° = 0
18° ∙ n - 360° = 0
Add 360° to both sides
18° ∙ n = 360°
n = 360° / 18°
n = 20