Question

Determine the number of sides of a polygon whose exterior and interior angles are in the ratio of 1:5

Answer 1

Ratio of external and internal angles = 1:5

Let, exterior angle be = 1x

interior angle be = 5x

Now, 1x + 5x = 180

6x = 180

x = 30

So exterior angle = 1x = 1×30 = 30°

interior angle = 5x = 5×30 = 150°

No. of sides of polygon = 360/exterior angle

=360/30 = 12

So, polygon is of 12 sides.