Question

practice with the measures of interior and exterior angles of polygons. in the regular decagon shown, what is the measure of angle 1? 18 36 72 180

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, the measure of each exterior angle \(E=\frac{360^{\circ}}{n}\).

Step2: Identify the number of sides of a decagon

A decagon has \(n = 10\) sides.

Step3: Calculate the measure of the exterior angle

Substitute \(n=10\) into the formula \(E=\frac{360^{\circ}}{n}\). So \(E=\frac{360^{\circ}}{10}=36^{\circ}\).

Answer:

\(36\)