Question

Find the number of sides of a regular polygon if the measure of an interior angle is 157.5°

Answer 1

In a polygon with n sides, the sum of the measures of the interior angles, S, is

$S = (n - 2)180$

In a regular polygon with n sides, the measure of each interior angle, a, is the sum of the measures of the interior angles divided by the number of sides, or

$a = \dfrac{(n - 2)180}{n}$

In this case, we know the measure of one angle, a = 157.5°, so we plug it into the second formula and solve for n.

$a = \dfrac{(n - 2)180}{n}$

$157.5 = \dfrac{(n - 2)180}{n}$

$157.5n = (n - 2)180$

$157.5n = 180n - 360$

$-22.5n = -360$

$n = 16$

Answer: The polygon has 16 sides.