Question

In a regular polygon the ratio of an interior and an exterior angle ia 7:2 . the number of sides will be

Answer 1

9.it will be since sum.of inerior and exterior angle will be 180 for a ploygon so solving we get interior angle 140 and exterior 40
now sum.of exterior angle of a polygon is 360
so that makes up 9 sides or a nonagon

Answer 2

Let the common multiple be x

Therefore, 2x + 7x = 180° [ Interior angle + Exterior angle = 180° ]

9x = 180

x = 180/9

20

Therefore interior angle = 140°

Exterior angle = 40°

No. of sides = 360/40

= 9