SOLUTION: The measure of each interior each interior angle of a regular polygon is 36 more than its adjacent exterior angle. How many sides has the polygon? Thanks!

Question 208221: The measure of each interior each interior angle of a regular polygon is 36 more than its adjacent exterior angle. How many sides has the polygon? Thanks!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The measure of each interior angle of a regular polygon is 36 more than its adjacent exterior angle. How many sides has the polygon? Thanks!
---------------------------
The two angles are supplementary.
So interior = exterior + 36
x = (180-x)+36
x = 90+18 = 108
Therefore the exterior angle is 180-108 = 72
---------------------------
The sum of the exterior angles is 360
# of exterior angles is 360/72 = 5
---
So the # of sides is 5.
==================================
Cheers,
Stan H.
RELATED QUESTIONS
Each interior angle of a regular polygon is 20 more than 3 times the measure of each... (answered by stanbon)

The measure of each interior angle of a regular polygon is 3 times larger than each... (answered by Alan3354)

each interior angle of a regular polygon is 140. what does each exterior angle... (answered by Alan3354)

The measure of each interior angle of a regular polygon is 20 degrees more than 3 times... (answered by stanbon)

The measure of each interior angle of a regular polygon is 20 degrees more than three... (answered by KMST)

{{{The measure of each interior angle of a regular polygon is three times the measure of... (answered by Alan3354)

If the measure of each interior angle of a regular polygon is five times the measure of... (answered by stanbon)

The measure of each exterior angle of a regular polygon is (2/3) that of an interior... (answered by Alan3354)

The measure of each interior angle of a regular polygon is 14 times the measure of an... (answered by solver91311)