Question

Find the number of sides a polygon has if the sum of the measures of its interior angles is four times the sum of the measures of its exterior angles.

Answer 1

Answer:

the polygon has 10 sides

Step-by-step explanation:

Recall that the sum of the interior angles of a polygon of N sides is given by the formula:

Sum = (N - 2) * 180

and that the sum of the exterior angles of any polygon is always 360 degrees.

Since we are told that the sum of the interior angles is 4 times the sum of the exterior angles, we set the following equation:

(N - 2) * 180 = 4 * 360

Solving for N, we start by dividing both sides by 180:

(N- 2) = 4 * 360 / 180

N - 2 =4 * 2

N - 2 = 8

N = 10

So the polygon has 10 sides