Question

each interior angle of a regular polygon is double of its exterior angle.find the number of sides in the polygon

Answer 1

6 sides... So each interior angle will be 120° and each exterior angle will be 240° (which just double of the interior angle.)

Answer 2

Let the exterior angle be x.

Then the interior angle will be double to its exterior angle = 2x.

Then x + 2x = 180

          3x = 180

          x = 60.

Therefore exterior angle = 60.

We know that the size of an exterior angle for a regular polygon = 360/n

 = 360/60

= 6.

Therefore the number of sides in the polygon = 6.


Hope this helps!