Question

The measure of an interior angle of a regular polygon is 90. Find the number of sides in the polygon. Enter your answer as a number.

Answer 1

The number of sides in polygon is 4

Solution:

Given that measure of an interior angle of a regular polygon is 90

To find: number of sides in polygon

The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180

S = 180(n - 2)

Measure of interior angle = 90

Therefore, for "n" sides we get,

S = 90n

Therefore,

90n = 180(n - 2)

90n = 180n - 360

90n - 180n = -360

-90n = -360

90n = 360

`n = (360)/(90) = 4`

Thus the number of sides in polygon is 4