Question

The measure of each interior angle is twice the measure of an exterior angle, how may sides does the regular polygon have?

Answer 1

6

Answer 2

The sum of the exterior angles of a regular polygon is 360. If the polygon has n sides, each exterior angle is 360/n. The problem says that the interior angle is twice the exterior angle but the interior angle is supplementary to the exterior angle. So the interior angle is 180-360/n. And so:

Answer 3

\[2(\frac{360}{n})=180-\frac{360}{n}\]

Answer 4

n is the number of sides, by the way.

Answer 5

In the regular polygon, an interior angle and an exterior angle form a linear pair.