Question

a regular polygon is such that its interior angle exceeds its exterior angle by 132°. Find sum of all the interior angles of the polygon​

Answer 1

2340°

Explanation:

In any polygon

interior angle + exterior angle = 180°

Here the interior angle = exterior angle + 132, then

exterior + 132 + exterior = 180 ( subtract 132 from both sides )

2 exterior = 48° ( divide both sides by 2 )

exterior angle = 24°

The sum of the exterior angles = 360°

Divide by 24 to find number of sides (n ) in the polygon

n = 360 ÷ 24 = 15

The sum of the interior angles is

sum = 180° (n - 2) ← n is the number of sides, thus

sum = 180° × 13 = 2340°