Question

A regular polygon has each interior angle equal to 140 degree if its area is 625 CM square find the length of its side

Answer 1

Answer:

We can tackle this problem in two ways.

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.