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The measure of one interior angle of a regular polygon is 157.5 find the number of sides

User Ruzard
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1 Answer

1 vote
we know that

One interior angle of a polygon is found by the equation:
A=(n-2)*180/n
where
A-----> interior angle of a polygon
n-----> the number of sides of the polygon

in this problem
A=157.5
°
A=(n-2)*180/n-----> A*n=180*n-360----> 180*n-A*n=360
n*[180-A]=360
n=360/[180-A]-----> n=360/[180-157.5]----> n=16

the answer is
the number of sides is 16
User Rmannn
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