Two adjacent angles of a parallelogram are in the ratio 4 : 5.

Question:

Two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure of each of its angles.

Solution:

Let $A B C D$ be the parallelogram.

Then, $\angle A$ and $\angle B$ are its adjacent angles.

Let $\angle A=(4 x)^{\circ}$

$\angle B=(5 x)^{\circ}$

$\therefore \angle A+\angle B=180^{\circ} \quad\left[s\right.$ ince sum of the adjacent angles of a parallelogram is $\left.180^{\circ}\right]$

$\Rightarrow 9 x=180$

$\Rightarrow x=\frac{180}{9}$

$\Rightarrow x=20$

$\therefore \angle A=(4 \times 20)^{\circ}=80^{\circ}$

$\angle B=(5 \times 20)^{\circ}=100^{\circ}$

$O$ pposite angles of parallelogram are equal.

$\therefore \angle C=\angle A=80^{\circ}$

$\angle D=\angle B=100^{\circ}$

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