5.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.

As per the given conditions, let ABCD be parallelogram such that
m∠B : m∠C = 3 : 2



So,let m∠B = \(3x^{\circ}\) and m∠C = \(2x^{\circ}\)

m∠B + m∠C = \(180^{\circ}\quad\) [Sum of adjacent angles = \(180^{\circ}\)]

\(\Rightarrow 3x + 2x = 180^{\circ}\)

\(\Rightarrow 5x = 180^{\circ}\)

\(\Rightarrow x = 36^{\circ}\)

Thus,\(∠B = 3 \times 36 = 108^{\circ}\)

\(∠C = 2 \times 36^{\circ}\) = \(72^{\circ}\)

\(∠B = ∠D = 108^{\circ}\)

and \(∠A = ∠C = 72^{\circ}\)

Hence, the angles of the parallelogram are \(108^{\circ}\), \(72^{\circ}\), \(108^{\circ}\) and \(72^{\circ}\).