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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 $156^o$.
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