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The angels of a quadrilateral are in the ratio 3 : 5 : 7 : 9, find the measure of each of these angles.
Given :
The angles of a quadrilateral are in the ratio $3:5:7:9$.
To do :
We have to find the measure of the angles.
Solution :
Let the angles be $3x, 5x, 7x$ and $9x$. (Since $3x:5x:7x:9x=3:5:7:9$)
We know that,
The sum of the angles in a quadrilateral is 360 degrees.
Therefore,
$3x+5x+7x+9x=360$ degrees
$24x=360^o$
$x= \frac{360^o}{24}$
$x=15^o$.
The measure of the angles is $3(15^o)=45^o$, $5(15^o)=75^o$, $7(15^o)=105^o$ and $9(15^o)=135^o$.
Therefore, the measure of the angles is $45^o, 75^o, 105^o, 135^o$.
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