Question

what is the measure of each interior angle of a regular 20 - gon in degrees?

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

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

Step2: Calculate the sum of interior angles

Substitute \( n = 20 \) into the formula: \( S=(20 - 2)\times180^{\circ}=18\times180^{\circ}=3240^{\circ} \).

Step3: Find the measure of each interior angle

In a regular polygon, all interior angles are equal. So, to find the measure of each interior angle, we divide the sum of the interior angles by the number of sides \( n \). That is, each interior angle \( A=\frac{S}{n} \). Substituting \( S = 3240^{\circ} \) and \( n = 20 \), we get \( A=\frac{3240^{\circ}}{20}=162^{\circ} \).

Answer:

\( 162^{\circ} \)