Question

(polygon angle sums mc)
a 20 - sided regular polygon has an angle measure represented as ( 3g^{circ} ).
determine the value of ( g ).
( g = 180 )
( g = 162 )
( g = 60 )
( g = 54 )

Explanation:

Step1: Find the sum of interior angles of a 20 - sided polygon

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

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

Step2: Find the measure of one interior angle

Since it is a regular polygon, all interior angles are equal. The measure of one interior angle \(A=\frac{S}{n}\).

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

Step3: Solve for \(g\)

Given that the angle measure is \(3g^{\circ}\), and \(3g = 162\).

$$g=\frac{162}{3}=54$$

Answer:

\(g = 54\) (the fourth option)