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 \(72 \degree\).