Question

Determine the number of sides of polygon whose exterior and interior angel are in the ratio 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.

I hope it helps u...

Answer 2

=>360° /(2n-4)= 1/5
=>4/(2n-4)=1/5
=>20=(2n-4)
=>2n=24
=>n=24/2
=>n=12