Question

The angles of a pentagon are in the ratio 5:4:5:7:6 ; find each angle of the pentagon.

Answer 1

The sum of the interior angle of pentagon can be calculated as,
(2n−4)×90^∘ = (2×5−4)×90^∘ = 6×90^∘

We get,=540^∘

The sum of interior angles of pentagon=540^∘

27x=540^∘

x=540^∘/27

We get,

x=20^∘

Thus, each angle,5x = 5×20^∘ = 100^∘

4x = 4×20^∘ = 80^∘

7x = 7×20^∘ = 140^∘

6x = 6×20^∘ = 120^∘
Therefore, all the angles of a pentagon are 100^∘,80^∘,100^∘,140^∘ and 120^∘