Question

A regular polygon has n sides
Each exterior angle is 5n/2 degrees
Find the value of n

Answer 1

 7a=interior angle
2a=exterior angle
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7a+2a=180
9a=180
a=20
So,
2a=40
7a=140
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For a regular polygon of n sides, each exterior angle has a measure of 360/n degrees.
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The measure of each interior angle is 140 degrees
Since the exterior angle of each angle has measure 40 degrees, then the number of sides n=360/40=9 sides.