The angles of a quadrilateral are in the ratio `3:5: 9:13.` Find all the angles of the quadrilateral.

Options

A. `A = 36^(@), angle B=50^(@), angle C= 108^(@) and angle D= 156^(@).`
B. `A = 36^(@), angle B=60^(@), angle C= 180^(@) and angle D= 156^(@).`
C. `A = 36^(@), angle B=60^(@), angle C= 108^(@) and angle D= 150^(@).`
D. `A = 36^(@), angle B=60^(@), angle C= 108^(@) and angle D= 156^(@).`

Answer

D

Explanation

Let ABCD be the given quarillateral and let
`angle A =(3x)^(@), angle B =(5x)^(@), angle C =(9x)^(@) and angle D = (13x)^(@).`
Since the sum of the angles of a quadrilateral is `360^(@)`, we have
`3x+5x+9x+13x=360 rArr 30x=360 rArr x = 12.`
`therefore angle A = 36^(@), angle B=60^(@), angle C= 108^(@) and angle D= 156^(@).`