Question

what is the measure of an exterior angle in a regular polygon with 13 sides? write your answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

Step1: Recall the formula for the measure of an exterior angle of a regular polygon.

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

Step2: Substitute \(n = 13\) into the formula.

Here, \(n = 13\), so we calculate \(\theta=\frac{360}{13}\approx27.7\) (rounded to the nearest tenth).

Answer:

\(27.7\)