Question

what is the measure of an exterior angle in a regular 16-gon? 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 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: Identify the number of sides \(n\) for the regular 16 - gon.

Here, \(n = 16\) (since it is a 16 - gon).

Step3: Calculate the measure of the exterior angle.

Substitute \(n = 16\) into the formula \(\theta=\frac{360^\circ}{n}\). So, \(\theta=\frac{360^\circ}{16}\)
\(\frac{360}{16}=22.5\)

Answer:

\(22.5^\circ\)