Find the number of sides of a regular polygon in which the measure of an interior angle is three times the measure of an exterio

Question

Dmitry_Shevchenko [17]

2 years ago

5

Find the number of sides of a regular polygon in which the measure of an interior angle is three times the measure of an exterio

r angle.

Mathematics

1 answer:

Serhud [2] · Answer 1 · 2022-12-28T06:15:06+03:00

Serhud [2]2 years ago

6 0

The sum of the interior angles of any polygon is given by (n-2)180°, where n is the number of sides.

Also sum of all the exterior angles of any polygon is 360°

Given (n-2)180° = 3(360°)

=> n-2 = 6

=> n = 8.

Hence the number of sides of a polygon is 8