Question

The number of sides of a regular polygon whose interior angle is 140​

Answer 1

9

Explanation:

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

Thus the exterior angle of the polygon = 180° - 140° = 40°

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

number of sides = 360° ÷ 40° = 9

Answer 2

9 sides

Explanation:

Two methods and the same answer = 9 sides

Method 1: Since the interior angle 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.

Method 2: Since the exterior angle 140 degrees, The sum of the interior angles = (2n - 4)* right angles. So 140n =(2n - 4)* right angles, or

140n =(2n - 4)*90, or

140n = 180n - 360, or

40n = 360, or

n = 9 sides.

Hence the number of sides is 9 sides.