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
