Question

A 30-sided regular polygon has an angle measure represented as 6g.

Determine the value of g

g = 30
g = 28
g = 180
g = 168

Answer 1

28

Explanation:

The sum of the interior angles of a polygon with n sides is given by the formula (n-2) × 180 degrees.

For a regular polygon with n sides, each angle has the same measure, so we can find the measure of each angle by dividing the sum of the interior angles by n.

In this case, we are given that the polygon has 30 sides and that the measure of each angle is 6g. Therefore, we can write:

(n-2) × 180 = n × 6g

Substituting n = 30, we get:

(30-2) × 180 = 30 × 6g

28 × 180 = 180g

g = (28 × 180) / 180 = 28

Therefore, the value of g is 28.