The four angles of a quadrilateral are as 3 : 5 : 7 : 9.

Question:

The four angles of a quadrilateral are as 3 : 5 : 7 : 9. Find the angles.

Solution:

Let the angles be in the ratio $3 x: 5 x: 7 x: 9 x$.

Since, the sum of all the angles of a quadrilateral is $360^{\circ}$, we have:

$3 x+5 x+7 x+9 x=360^{\circ}$

$\Rightarrow 24 x=360^{\circ}$

$\Rightarrow x=15^{\circ}$

Thus, the angles are:

$3 x=45^{\circ}$

$5 x=75^{\circ}$

$7 x=105^{\circ}$

$9 x=135^{\circ}$

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