Question

find the measure of an interior angle of a regular icosagon (20 - sided polygon). hint: sum = (n - 2)180

Explanation:

Step1: Calculate the sum of interior angles

The formula for the sum of interior angles of a polygon is \(Sum=(n - 2)\times180^{\circ}\), where \(n = 20\) (for icosagon).

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

Step2: Find the measure of one interior angle

Since it is a regular icosagon (all interior angles are equal), divide the sum by \(n\).

$$x=\frac{3240^{\circ}}{20}=162^{\circ}$$

Answer:

\(162\)