Question

In a regular polygon each interior angle is 140° greater than each exterior angle. Calculate the number of sides of the polygon​

Answer 1

18 sides.

Explanation:

The interior and exterior angles sum to 180 so:

I + E = 180

also I - E = 140 (given)

So, adding to eliminate E:

2I = 320

I = 160 degrees and the external angle E = 1809 - 160 = 20 degrees.

Since the sum of all exterior angles in a polygon = 360 degrees

- the number of sides = 360 / 20 = 18.