Question

The measures of two adjacent angles of a parallelogram are in the ratio $3:2$. Find the measure of each of the angles of the parallelogram.

Answer 1

The measure of each of the angles of the parallelogram

Let the measures of two adjacent angles are $3x$ and $2x$.

As the sum of two adjacent angles of a parallelogram is $180°$.

Then,

$$\begin{gathered} 3x+2x=180°\left[\because \mathrm{that}\mathrm{are}\mathrm{in}\mathrm{the}\mathrm{ratio}3:2\right] \\ \Rightarrow 5x=180° \\ \therefore x=36° \end{gathered}$$

Now,

$$\begin{gathered} 3x=3\times 36° \\ =108° \\ 2x=2\times 36° \\ =72° \end{gathered}$$

The opposite angles of a parallelogram are equal. So, a measure of each of the angles of a parallelogram is

$108°,72°,108°,72°$.

Hence, the measure of each of the angles of a parallelogram is

$108°,72°,108°,72°$.