Question

an exterior angle and the interior angle of a regular polygon Are in the ratio 3 and 6find the no. of sides of the polygon

Answer 1

Interior angle + exterior angle = 180º

Define x:

Ratio of interior angle : exterior angle = 3 : 6

Let x be the constant ratio

Ratio of interior angle : exterior angle = 3x : 6x

Form equation and solve for x:

3x + 6x = 180

9x = 180

x = 180 ÷ 9 = 20º

Find one exterior angle:

exterior angle = 6x = 6(20) = 120º

Find the number of sides:

Sum of all the exterior angles = 360º

Number of sides = 360 ÷ 120 = 3

Answer: The polygon has 3 sides, which is a triangle.