Question

what is the measure of one interior angle of a regular 26 - gon?
≈166.2°
165°
165.6°
≈166.7°

Explanation:

Step1: Recall sum - of - interior - angles formula

The sum of the interior angles of a polygon is given by $S=(n - 2)\times180^{\circ}$, where $n$ is the number of sides. For a 26 - gon, $n = 26$. So $S=(26 - 2)\times180^{\circ}=24\times180^{\circ}=4320^{\circ}$.

Step2: Find measure of one interior angle

Since the 26 - gon is regular, all interior angles are equal. Let $x$ be the measure of one interior angle. Then $x=\frac{S}{n}=\frac{4320^{\circ}}{26}\approx166.2^{\circ}$.

Answer:

A. $\approx 166.2^{\circ}$