Question

question 2 (2 points)
what is the measure of one interior angle of a regular 20 - gon?
o a 162°
o b 135°
o c 122°
o d 144°

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, \(n = 20\).

$$S=(20 - 2)\times180^{\circ}=18\times180^{\circ}=3240^{\circ}$$

Step2: Find the measure of one interior angle

Since the 20 - gon is regular (all interior angles are equal), divide the sum of interior angles by the number of sides \(n\).
\(\theta=\frac{3240^{\circ}}{20}=162^{\circ}\)

Answer:

A. \(162^{\circ}\)