Question

1. what is the measure of each exterior angle of a regular 20 - gon?

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 if the polygon has \(n\) sides, each exterior angle \(\theta\) is given by the formula \(\theta=\frac{360^\circ}{n}\).

Step2: Substitute \(n = 20\) into the formula

Here, the polygon is a regular 20 - gon, so \(n = 20\). Substituting \(n = 20\) into the formula \(\theta=\frac{360^\circ}{n}\), we get \(\theta=\frac{360^\circ}{20}\).

Step3: Calculate the value

\(\frac{360^\circ}{20}=18^\circ\).

Answer:

The measure of each exterior angle of a regular 20 - gon is \(18^\circ\).