Question:
The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. Find the measure of each of these angles.
Solution:
Let the measures of the angles of the given quadrilateral be $(3 x)^{\circ},(5 x)^{\circ},(7 x)^{\circ}$ and $(9 x)^{\circ}$.
Sum of all the angles of a quadrilateral is $360^{\circ}$.
$\therefore 3 x+5 x+7 x+9 x=360$
$24 x=360$
$x=15$
Angles measure:
$(3 \times 15)^{\circ}=45^{\circ}$
$(5 \times 15)^{\circ}=75^{\circ}$
$(7 \times 15)^{\circ}=105^{\circ}$
$(9 \times 15)^{\circ}=135^{\circ}$