Question

if each interior angle of a regular polygon measures 157.5°, how many sides does it have?
a. 12 sides
b. 17 sides
c. 14 sides
d. 16 sides
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Explanation:

Step1: Find exterior angle measure

The interior and exterior angles of a polygon are supplementary, so:
$180^\circ - 157.5^\circ = 22.5^\circ$

Step2: Use total exterior angle sum

The sum of exterior angles of any polygon is $360^\circ$. Let $n$ = number of sides.
$n = \frac{360^\circ}{\text{measure of one exterior angle}}$
$n = \frac{360}{22.5}$

Step3: Calculate the number of sides

$n = 16$

Answer:

D. 16 sides