Question

15 what is the interior and exterior angle measures for a regular octagon? a 45 b 67.5 c 135 d 60 e 120 hide hint

Explanation:

Step1: Recall exterior - angle formula

The sum of exterior angles of any polygon is 360°. For a regular polygon with \(n\) sides, the measure of each exterior angle \(\theta_{e}=\frac{360^{\circ}}{n}\). An octagon has \(n = 8\) sides. So, \(\theta_{e}=\frac{360^{\circ}}{8}=45^{\circ}\).

Step2: Recall interior - exterior angle relationship

The interior angle \(\theta_{i}\) and exterior angle \(\theta_{e}\) of a polygon at a vertex are supplementary, i.e., \(\theta_{i}+\theta_{e}=180^{\circ}\). Since \(\theta_{e} = 45^{\circ}\), then \(\theta_{i}=180^{\circ}-\theta_{e}=180 - 45=135^{\circ}\).

Answer:

Exterior angle: A. 45, Interior angle: C. 135