Two adjacent angles of a parallelogram are in the ratio 2 : 3.

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 $108^{\circ}$.

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