Question 785529

Each exterior angle is 100º less than its interior angle of a regular polygon. Find the number of sides of the polygon.

Thank you!


Let measure of each exterior angle be E
Then measure of each interior angle  = E + 100


Since both angles are supplementary, then: E + E + 100 = 180


2E = 180 - 100


2E = 80


E, or measure of each exterior angle = {{{80/2}}}, or {{{40^o}}}


Since the sum of the measures of the exterior angles of ALL polygons is {{{360^o}}}, and with each exterior angle of this REGULAR polygon being {{{40^o}}}, then the number of sides of this polygon = {{{360/40}}}, or {{{highlight_green(9)}}}