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

Solution:

Let the common ratio between the angles be $x$. Therefore, the angles will be $3 x, 5 x, 9 x$, and $13 x$ respectively.

As the sum of all interior angles of a quadrilateral is $360^{\circ}$,

$\therefore 3 x+5 x+9 x+13 x=360^{\circ}$

$30 x=360^{\circ}$

$x=12^{\circ}$

Hence, the angles are

$3 x=3 \times 12=36^{\circ}$

$5 x=5 \times 12=60^{\circ}$

$9 x=9 \times 12=108^{\circ}$

$13 x=13 \times 12=156^{\circ}$