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the measure of the interior angle of a convex polygon is 4 times the measure of its exterior angle on same vertex. What is the measure of the exterior angle?

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Answer:

Q: The interior angle of a regular polygon is four times its exterior angle. What is the number of sides?

A: Let exterior angle = x => Interior angle = 4x

x + 4x = 180°

x = 180/5 = 36° ; Exterior angle

Since sum of exterior angles = 360°,

No. of sides = 360/x = 360 ÷ 36 = 10 sides

No of sides for specified angles = 10

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