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:
$3 x=45^{\circ}$
$5 x=75^{\circ}$
$7 x=105^{\circ}$
$9 x=135^{\circ}$