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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Updated on: 10-Oct-2022

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