Question

the size of an interior angle of a rectangular polygon is(3x)⁹ while the exterior angle is (X-20)⁰.find the number of side of the polygen.

Answer 1

12 sides

Explanation:

The sum of the exterior angle and the interior angle = 180° , then

3x + x - 20 = 180

4x - 20 = 180 ( add 20 to both sides )

4x = 200 ( divide both sides by 4 )

x = 50

Then

exterior angle = x - 20 = 50 - 20 = 30°

The sum of the exterior angles of a polygon = 360°

The number of sides n is sum divided by 1 exterior angle , that is

n = 360° ÷ 30° = 12