Question

Find the sum of the measures of the interior angles of a regular 30-gon. Then find the measure of each interior angle and each exterior angle.

Answer 1

(a) 5040°

(b) 168°

(c) 12°

Explanation:

(a) The sum of angles in a polygon of N sides is given as:

S = (N - 2) * 180

For a 30-gon, N = 30.

Therefore, the sum of the angles in the 30-gon will be:

S = (30 - 2) * 180

S = 28 * 180

S = 5040°

(b) To find each interior angle, we simply divide S by 30:

Interior Angle = 5040/30

Interior Angle = 168°

(c) Each exterior angle of a polygon is gotten by subtracting the interior angle from 180°.

Hence, each exterior angle is:

180 - 168 = 12°