Question

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

Answer 1

Let the angles be 3x,5x,9x and 13x
So, by angle sum property of quadrilateral

$3x + 5x + 9x + 13x = 360$
$30x = 360 \\ x = 360 \div 30 \\ x = 12$
Largest angle = 13x = 13 * 12 = 156

Answer 2

Let the angles be 3x ,5x, 9x,13x

so 3x + 5x + 9x + 13x = 360
⇒ x = 12
so the angles are 3×12 , 5×12 , 9× 12 , 13×12

i.e. 36,60,108,156