Find the number of sides for a regular polygon in which each interior angle is 120° larger than each exterior angle.
A) 9
B) 12
C) 15
D) 18

Question

Quizplus · Accepted Answer

Let's use the formula for the sum of the interior angles of a polygon:

Sum of interior angles = (n - 2) * 180

where n is the number of sides.

We know that each interior angle is 120° larger than each exterior angle. We can express this as:

interior angle = exterior angle + 120°

We also know that the sum of exterior angles of a polygon is always 360°. So we can write:

n * exterior angle = 360°

Using these two equations, we can solve for interior angle and substitute it into the formula for sum of interior angles:

interior angle = exterior angle + 120°
interior angle + exterior angle = 180° (since they are supplementary angles)
2 * exterior angle + 120° = 180°
2 * exterior angle = 60°
exterior angle = 30°

Substituting this value of exterior angle into the equation for the sum of exterior angles, we get:

n * 30° = 360°
n = 12

Therefore, the regular polygon has 12 sides, and the answer is B.

Find the Number of Sides for a Regular Polygon in Which