Question

what is the measure of each interior angle of a regular octagon? 60° 135° 120° 45°

Explanation:

Step1: Recall the formula for the sum of interior angles

The sum of interior angles of a polygon is $S=(n - 2)\times180^{\circ}$, where $n$ is the number of sides. For an octagon, $n = 8$.
$$S=(8 - 2)\times180^{\circ}=6\times180^{\circ}=1080^{\circ}$$

Step2: Find the measure of each interior angle

Since it is a regular octagon (all interior angles are equal), divide the sum by the number of sides. Each interior angle $A=\frac{S}{n}$.
$$A=\frac{1080^{\circ}}{8}=135^{\circ}$$

Answer:

B. \(135^{\circ}\)