# Two adjacent angles of a parallelogram are as 1 : 2.

Question:

Two adjacent angles of a parallelogram are as 1 : 2. Find the measures of all the angles of the parallelogram.

Solution:

Let the angle be $\mathrm{A}$ and $\mathrm{B}$.

The $a$ ngles are in the ratio of $1: 2$.

$M$ easures of $\angle \mathrm{A}$ and $\angle \mathrm{B}$ are $\mathrm{x}^{\circ}$ and $2 \mathrm{x}^{\circ}$.

Then, $\angle \mathrm{C}=\angle \mathrm{A}$ and $\angle \mathrm{D}=\angle \mathrm{B}(o$ pposite angles of $a$ parallelogram are congruent $)$

As we know that the sum of adjacent angle $s$ of a parallelogram is $180^{\circ}$.

$\therefore \angle \mathrm{A}+\angle \mathrm{B}=180^{\circ}$

$\Rightarrow \mathrm{x}^{\circ}+2 \mathrm{x}^{\circ}=180^{\circ}$

$\Rightarrow 3 \mathrm{x}^{\circ}=180^{\circ}$

$\Rightarrow \mathrm{x}^{\circ}=\frac{180^{\circ}}{3}=60^{\circ}$

Thus, measure of $\angle \mathrm{A}=60^{\circ}, \angle \mathrm{B}=120^{\circ}, \angle \mathrm{C}=60^{\circ}$ and $\angle \mathrm{D}=120^{\circ}$.