Question

find the measure of each interior angle and each exterior angle of a regular 20 - gon (a twenty - sided polygon).
measure of each interior angle = \\(\square^\circ\\)
measure of each exterior angle = \\(\square^\circ\\)

Explanation:

Step1: Find the sum of interior angles

The formula for the sum of interior angles of a polygon is \((n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For a 20 - gon, \(n = 20\). So the sum of interior angles is \((20 - 2)\times180^{\circ}=18\times180^{\circ} = 3240^{\circ}\).

Step2: Find each interior angle

Since the polygon is regular, all interior angles are equal. So each interior angle is \(\frac{(20 - 2)\times180^{\circ}}{20}=\frac{3240^{\circ}}{20}=162^{\circ}\).

Step3: Find each exterior angle

The sum of exterior angles of any polygon is \(360^{\circ}\). For a regular polygon, each exterior angle is \(\frac{360^{\circ}}{n}\). For \(n = 20\), each exterior angle is \(\frac{360^{\circ}}{20}=18^{\circ}\).

Answer:

Measure of each interior angle = \(162^{\circ}\)
Measure of each exterior angle = \(18^{\circ}\)