Quick! HELP! THANK YOU SO MUCH! If the difference between the interior and exterior angles of a regular polygon is 100°, how many sides does the polygon have?

Question

asked Jan 23, 2022 149k views

2 Answers

Alex Fung · Answer 1 · 2022-01-28T11:15:10+0000

Answer:

9 sides

Explanation:

Sum of the measures of the interior angle of a polygon with n sides:

(n - 2)180

Measure of 1 interior angle of a regular polygon of n sides:

(n - 2)180/n

Sum of the measures of the exterior angles of a polygon, one per vertex:

360

Measure of 1 exterior angle of a regular polygon of n sides:

360/n

(n - 2)180/n = 360/n + 100

Multiply both sides by n.

(n - 2)180 = 360 + 100n

Distribute on left side.

180n - 360 = 360 + 100n

Subtract 100n from both sides.

80n - 360 = 360

Add 360 to both sides.

80n = 720

Divide both sides by 80.

n = 9

Answer: 9 sides