Question

1. what is the measure of each exterior angle of a regular octagon?

(1) $45^circ$
(2) $90^circ$
(3) $135^circ$
(4) $180^circ$

Explanation:

Step1: Recall the formula for exterior angles of a regular polygon

For any regular polygon, the sum of the exterior angles is always \(360^\circ\). And for a regular polygon with \(n\) sides, each exterior angle \(\theta\) is given by the formula \(\theta=\frac{360^\circ}{n}\).

Step2: Determine the number of sides of an octagon

An octagon has \(n = 8\) sides.

Step3: Calculate the measure of each exterior angle

Substitute \(n = 8\) into the formula \(\theta=\frac{360^\circ}{n}\). So \(\theta=\frac{360^\circ}{8}=45^\circ\).

Answer:

(1) \(45^\circ\)