Question

The ratios between exterior angle and interior angle of a regular polygon is 1:5. Find the number of sides of the polygon

Answer 1

We know that, interior angle + exterior angle= 180

therefore let interior angle be= x

and exterior angle be = 5x

hence, 6x = 180

             x = 30

hence exterior angle = 1

this question isn't possible

Answer 2

ratio of each exterior and interior angle of a regular polygon = 1 : 5

let the constant ratio be 'x'

sum of each exterior and interior angles of a regular polygon = 360°

1x + 5x = 360

6x = 360 => x = 60°

each exterior angle of this regular polygon
= 1x = 1 × 60 = 60°

number of sides

= 360°/ 60° = 6 sides

Answer:
_______

number of sides of the polygon will be 6 .