Question

What is the name of a polygon if the ratio of the interior to exterior angle is 7:2?

Answer 1

Since, interior angle + exterior angle of any polygon ,at one vertex = 180° & the given value of ratio of these angles = 7:2

let angle be 7x and 2x respectively

or, 7x + 2x = 180

or, 9x = 180

or, x = 20

therefore x = 140

Angle of a regular polygon = (n-2)180 / n , where n is the no of sides!

or, (n-2)*180 / n = 140

or, 180n - 140n = 360

or, 40n = 360

or, n = 9

therefore, It is a regular nonagone!!