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

Given:

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

To do:

We have to find the measures of each angle of the quadrilateral.

Solution:

We know that,

The sum of the angles in a quadrilateral is $360^o$.

Let the angles of the quadrilateral be $3x, 5x, 9x$ and $13x$ respectively.

Therefore,

$3x+5x+9x+13x=360^o$

$30x=360^o$

$x=\frac{360^o}{30}$

$x=12^o$

This implies,

$3x=3(12^o)=36^o$

$5x=5(12^o)=60^o$

$9x=9(12^o)=108^o$

$13x=13(12^o)=156^o$

Hence, the measures of each angle of the quadrilateral are $36^o, 60^o, 108^o$ and $156^o$.