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

Sum of the four angles of a quadrilateral = ${360}^{\circ }$

Let first angle = 3x

Then second angle = 5x

Third angle = 9x

and fourth angle = 13 x

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

$\Rightarrow$ $30x={360}^{\circ }\Rightarrow x=\frac{{360}^{\circ }}{{30}^{\circ }}={12}^{\circ }$

$\therefore Firstangle=3x=3\times {12}^{\circ }={36}^{\circ }Secondangle=5x=5\times {12}^{\circ }={60}^{\circ }Thirdangle=9x=9\times 12={108}^{\circ }Fourthangle=13\times {12}^{\circ }={156}^{\circ }$