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# 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 $$72^{\circ}$$.