Question

the ratio of an Interior angle to the exterior angle of a regular polygon is 7:2 the number of sides of the polygon is​

Answer 1

Answer:

9 sides

Step-by-step explanation:

Let the interior and exterior angle be 7x and 2x

7x+2x=180°(linear pair)

9x=180°

x=180/9

x=20°

exterior angle=2x

=2(20°)

=40°

For a regular polygon

(no. of sides)×(each ext. angle)=360°

(no. of sides)×40°=360°

(no. of sides)=360°/40°

(no. of sides)=9