Question

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

Answer 1

Let the common ratio between the angle be x, therefore, the angles will be 3x,5x, 9x, and 13x respectively.
As the sum of all interior angles of a quadrilateral is ${360}^{\circ }$,
$\therefore$ 3x+5x+9x+13x=360${}^{\circ }$
$30x={360}^{\circ }$
$x={12}^{\circ }$
Hence, the angles are
$3x=3\times 12={36}^{\circ }$
$5x=5\times 12={60}^{\circ }$
$9x=9\times 12={108}^{\circ }$
$13x=13\times 12={156}^{\circ }$