Question

find the measure of an interior angle of a regular octagon (8 - sided polygon). x = ?° hint: sum=(n - 2)180

Explanation:

Step1: Calculate sum of interior angles

For an octagon, $n = 8$. Using the formula $S=(n - 2)\times180^{\circ}$, we have $S=(8 - 2)\times180^{\circ}=6\times180^{\circ}=1080^{\circ}$.

Step2: Find measure of one interior angle

Since it's a regular octagon, all interior angles are equal. So one interior angle $x=\frac{S}{n}=\frac{1080^{\circ}}{8}=135^{\circ}$.

Answer:

$135$