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

Let the measures of two adjacent angles, $∠A$ and $∠B$, of parallelogram $ABCD$ are in the ratio of $3:2$.
Let $∠A = 3x$ and $∠B = 2x$
We know that the sum of the measures of adjacent angles is $180 \degree$ for a parallelogram.
$∠A + ∠B = 180 \degree$
$\Rightarrow$ $3x + 2x = 180 \degree$
$\Rightarrow$ $5x = 180 \degree$
$\Rightarrow$ $x$ = $\frac{180\degree}{5}$
=$36°$
$∠A = ∠C = 3x = 108 \degree$ (Opposite angles)
$∠B = ∠D = 2x = 72 \degree$ (Opposite angles)

Thus, the measures of the angles of the parallelogram are $108 \degree$, $72 \degree$, $108 \degree$, and $72 \degree$.