A regular polygon has twice the number of sides as another regular polygon. The perimeter of the smaller polygon is 84.8 cm and each of its interior angles measures 140°. The side length of the larger polygon is 1.2 times that of the smaller one. What is the measure of each interior angle of the larger polygon?
Show answer & explanation
Correct answer: C
Explanation
Given:
Each interior angle of the smaller polygon = 140°
By the formula:
Interior angle = ((n − 2) × 180) / n
((n − 2) × 180) / n = 140
180n − 360 = 140n
40n = 360
n = 9
Sides of the larger polygon = 2n = 2 × 9 = 18
Interior angle = ((18 − 2) × 180) / 18 = 160°