Question:
Two adjacent angles of a parallelogram are in the ratio 2 : 3. Find the measure of each of its angles.
Solution:
Let the two adjacent angles of the parallelogram be $(2 x)^{\circ}$ and $(3 x)^{\circ}$.
Sum of any two adjacent angles of a parallelogram is $180^{\circ}$.
$\therefore 2 x+3 x=180$
$\Rightarrow 5 x=180$
$\Rightarrow x=36$
$(2 x)^{\circ}=(2 \times 36)^{\circ}=72^{\circ}$
$(3 x)^{\circ}=(3 \times 36)^{\circ}=108^{\circ}$
Measures of the angles are $72^{\circ}$ and $108^{\circ}$.