Question

The measure of each exterior angle of a regular polygon is 2/3 that of an interior angle. How many sides does the regular polygon have?

Answer 1

Make sure you explain how you get your answer.

Answer 2

Interior angle\[=\frac{(n-2)*180}{n}\]

Sum of all exterior angles=360

Angles of each exterior angle
\[=\frac{360}{n}\]

So,
Angles of each exterior angle=2/3 Interior angle
\[\frac{360}{n}=\frac{2}{3}*\frac{(n-2)*180}{n}\]
n=5

Answer 3

You understand?

Answer 4

Let x be the measure of the interior angle
Then, (2/3) x is the measure of the adjacent exterior angle.

x + (2/3)x = 180

(5/3)x = 180
x = 108 which is the measure of one interior angle
The adjacent exterior angle is 180 - 108 = 72.

You could crank out the 72 by taking (2/3) of 108.

The key here is knowing that the sum of the exterior angles is 360.

360 divided by 72 gives 5 which means there are 5 exterior angles, 5 interior angles, and 5 sides. This is a regular pentagon.