Question

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

Answer 1

Let the four angles of the quadrilateral be $3x,5x,9x$ and $13x$ respectively where $x$ is positive integer.

Now, we know, that sum of all the angles of a quadrilateral is ${360}^{\circ }$.

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

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

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

Therefore,

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

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

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

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

Hence, four angles of the quadrilateral are ${36}^{\circ },{60}^{\circ },{108}^{\circ },{156}^{\circ }$.