Question

If the exterior angle of a regular polygon is one fifth of its interior angle.How many sides does the polygon have ?

Answer 1

let the interior angle be x
exterior angle will be
(180- x )
(180 - x ) = 1x/5
900-5x = x
900= x + 5x
900= 6x
x = 900/6
x= 150
each interior angle is 150°
the number of sides are
{ n - 2 ) * 180} /n = 150
( n - 2 ) * 180 = 150n
n-2 = 150n / 180
n-2 = 5n/6
6(n - 2)= 5n
6n - 5n = 12
n = 12
number of sides= 12

Answer 2

Let exterior angle = x Interior angel = 5x X + 5x = 180 6x = 180 X = 180/6 X = 30 Exterior angle = 360/ no of sides  30 = 360 /no of sides No of sides = 360/30 No of sides = 12