Each interior angle of a regular polygon is 140°. Find the number of sides of the polygon.

9 sides

Explanation:

Step 1

Since the interior angle is 140 degrees, the supplement of this is the exterior angle and equal to 40 degrees. Hence the number of sides is 360/40 = 9 sides.

Step 2

Method 2: Since the exterior angle is 140°

The sum of the interior angles = (2n - 4) * right angles.

So 140n = (2n - 4) * right angles, or we can also say

140n = (2n - 4) * 90

140n = 180n - 360

40n = 360

Divide both sides of the equation by 40

n = 9 sides.

n = 9 sides. Hence the number of sides is 9 sides.