Question

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

Explanation:

Step1: Find the sum of interior angles

The formula for 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: Calculate the measure of each interior angle

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

Answer:

\(135^{\circ}\) (the fourth option)