The exterior angle of a regular polygon is two-third of its interior angle How many sides are there in - Maths - Understanding Quadrilaterals

Question

The exterior angle of a regular polygon is two-third of its
interior angle How many sides are there in the polygon??? I want
this ans with steps

Ajanta Trivedi · Accepted Answer

let the interior angle of the polygon be x.

therefore exterior angle of the polygon = $\frac{2}{3} x$

since interior angle and exterior angle are formed on the one side of a straight line.

therefore $x + \frac{2}{3} x = 180$

$\frac{5}{3} x = 180 x = \frac{3 * 180}{5} = 3 * 36 = 108$

therefore the interior angle of the regular polygon = 108 deg

let the number of sides of the polygon be n .

therefore sum of all the interior angles = (n-2)*180

since the angles of a regular polygon are equal.

therefore interior angle of the polygon = $\frac{(n - 2)}{n} * 180$

$\frac{n - 2}{n} * 180 = 108 \frac{n - 2}{n} * 5 = 3 [d i v i d i n g b y 36] 5 (n - 2) = 3 n 5 n - 10 = 3 n 5 n - 3 n = 10$

2n = 10

n =10/2 =5

thus the polygon has 5 sides.

hope this helps you.

cheers!!

The exterior angle of a regular polygon is two-third of its interior angle. How many sides are there in the polygon??? I want this ans. with steps......