SOLUTION: A regular polygon has an exterior angle measure of (x+3)degrees and an interior angle measure of (13x-33)degrees. 1. Find the measure of each angle. 2. How many sides does the

Algebra ->  Polygons -> SOLUTION: A regular polygon has an exterior angle measure of (x+3)degrees and an interior angle measure of (13x-33)degrees. 1. Find the measure of each angle. 2. How many sides does the       Log On


   

Question 689819: A regular polygon has an exterior angle measure of (x+3)degrees and an interior angle measure of (13x-33)degrees.
1. Find the measure of each angle.
2. How many sides does the polygon have?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The exterior and interior angles are supplementary (adding to 180%5Eo), so
%28x%2B3%29%2B%2813x-33%29=180 --> 14x-30=180 --> 14x=180%2B30 --> 14x=210 --> x=210%2F14 --> x=15
1. The measure of the exterior angle is
15%5Eo%2B3%5Eo=highlight%2818%5Eo%29
The measure of the supplementary interior angle is
180%5Eo-18%5Eo=highlight%28162%5Eo%29

2.The sum of all n exterior angles is 360%5Eo, so
18n=360 --> n=360%2F18 --> highlight%28n=20%29