Question

The interior angle of a pentagon are in the ratio 4:5:6:7:5 find each angle of the Pentagon
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Answer 1

Let the values of the angles of the Pentagon be x.

According to the question,

The angles of the Pentagon are 4x,5x,5x,6x,7x respectively.

The sum of the interior angles of the pentagon =( n -2) × 180°

=(5 - 2) × 180°

=540°

4x+5x+5x+6x+7x=540°

27x=540°

x=540°/27

x=20°

So the angles are

4x= 4×20 = 60°

5x= 5×20 = 100°

5x= 5×20 = 100°

6x=6×20 = 120°

7x=7×20 = 140°