Question

How many sides does a regular
polygon have if one interior
angle measures 160°?
n = [?]
Hint: The measure of each interior angle
in a regular n-gon is (n-2)180

Answer 1

If the measure of one interior angle be 160° then the sides of polygon be 18.

Given that the measure of one interior angle be 160°.

We are required to find the number of sides of polygon if the measure of one interior angle be 160°.

Polygon is basically a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

The interior angle of polygon is given by :

Angle=(n-2)*180/n

160=(180n-360)/n

160n=180n-360

180n-160n=360

20n=360

n=18

Hence if the measure of one interior angle be 160° then the sides of polygon be 18.

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