SOLUTION: In an equangular polygon, the measure of each exterior angle is 25% of the measure of each interior angle. What is the name of the polygon?

SOLUTION: In an equangular polygon, the measure of each exterior angle is 25% of the measure of each interior angle. What is the name of the polygon?

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Question 254060: In an equangular polygon, the measure of each exterior angle is 25% of the measure of each interior angle. What is the name of the polygon?
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Let x be the exterior angle
x/(180-x)=1/4 proportion
4x=180-x multiply each side by 4(180-x)
5x=180
x=36
180-36=144 interior angle
180(n-2)/n=144 the number of sides is n.
180n-360=144n
36n=360
n=10
The polygon is a decagon.
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