Question:
The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find the measure of each angle.
Solution:
Let the angles be $(x)^{\circ},(2 x)^{\circ},(3 x)^{\circ}$ and $(4 x)^{\circ}$.
Sum of the angles of a quadrilateral is $360^{\circ}$.
$x+2 x+3 x+4 x=360$
$10 x=360$
$x=\frac{360}{10}$
$x=36$
$(2 x)^{\circ}=(2 \times 36)^{\circ}=72^{\circ}$
$(3 x)^{\circ}=(3 \times 36)^{\circ}=108^{\circ}$
$(4 x)^{\circ}=(4 \times 36)^{\circ}=144^{\circ}$
The angles of the quadrilateral are $36^{\circ}, 72^{\circ}, 108^{\circ}$ and $144^{\circ}$.