Question

what is the measure of an exterior angle in a regular octagon? write your answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

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

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

Step2: Determine the number of sides of an octagon

A regular octagon has \(n = 8\) sides.

Step3: Calculate the measure of one exterior angle

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

Answer:

\(45\)