SOLUTION: The measure of an interior angle of an equiangular polygon is 45 more than two times the measure of one of the polygon's exterior angles. How many sides does the polygon have?

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Question 1160321: The measure of an interior angle of an equiangular polygon is 45 more than two times the measure of one of the polygon's exterior angles. How many sides does the polygon have?
Found 3 solutions by solver91311, Alan3354, MathTherapy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


The sum of the exterior angles of any convex polygon is

Hence the measure of one exterior angle of an -sided regular polygon is

Twice this value plus is then

The sum of the interior angles of a convex polygon is given by , so the measure of one interior angle of a regular polygon is

So, for this polygon:



Solve for


John

My calculator said it, I believe it, that settles it
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
The measure of an interior angle of an equiangular polygon is 45 more than two times the measure of one of the polygon's exterior angles. How many sides does the polygon have?
============================
Int = 2*Ext + 45
Int + Ext = 180
---
2Ext+45 + Ext = 180
Ext = 45
# of sides = 360/45 = 8
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

The measure of an interior angle of an equiangular polygon is 45 more than two times the measure of one of the polygon's exterior angles. How many sides does the polygon have?
Let measure of an exterior angle be E

Then measure of an interior angle = 2E + 45 

We then get: E + 2E + 45 = 180

3E = 135

Measure of an exterior angle, or 

With each exterior angle being 45o, number of sides/angles of the polygon is  

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