Question

select the correct answer.
a regular convex polygon has 16 sides. what is the measure of an interior angle?
a. 127.5°
b. 140°
c. 140.5°
d. 157.5°

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The sum of the interior angles of a polygon with \( n \) sides is given by \( S=(n - 2)\times180^{\circ} \). For a 16 - sided polygon, \( n = 16 \).
So, \( S=(16 - 2)\times180^{\circ}=14\times180^{\circ}=2520^{\circ} \).

Step2: Find the measure of one interior angle

In a regular polygon, all interior angles are equal. So, the measure of one interior angle \( \theta=\frac{S}{n} \).
Substituting \( S = 2520^{\circ} \) and \( n = 16 \), we get \( \theta=\frac{2520^{\circ}}{16}=157.5^{\circ} \).

Answer:

D. \( 157.5^{\circ} \)