Question

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

Answer 1

As we know that the sum of the four angles of a quadrilateral = ${360}^{\circ }$

Let first angle $=3x^{\circ }$

Then second angle $=5x^{\circ }$

Third angle $=9x^{\circ }$

and fourth angle $=13x^{\circ }$

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

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

Thus, the first angle $=3x=3\times {12}^{\circ }={36}^{\circ }$
Second angle $=5x=5\times {12}^{\circ }={60}^{\circ }$
Third angle$=9x=9\times {12}^{\circ }={108}^{\circ }$
Fourth angle$=13\times {12}^{\circ }={156}^{\circ }$