Themeasures of two adjacent angles of a parallelogram are in the ratio3:2 Find the measure of each of the - Maths - Understanding Quadrilaterals

Question

Themeasures of two adjacent angles of a parallelogram are in the
ratio3:2 Find the measure of each of the angles of the
parallelogram

Global Expert · Accepted Answer

Let themeasures of two adjacent angles, ∠Aand ∠B, of
parallelogramABCD are in the ratio of 3:2 Let ∠A= 3x
and ∠B = 2x
We knowthat the sum of the measures of adjacent angles is
180º for aparallelogram
∠A+ ∠B = 180º
3x+ 2x = 180º
5x= 180º
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∠A= ∠C = 3x = 108º (Opposite angles)
∠B= ∠D = 2x =72º (Opposite angles)
Thus, themeasures of the angles of the parallelogram are
108º, 72º,108º, and 72º

Themeasures of two adjacent angles of a parallelogram are in the ratio3:2. Find the measure of each of the angles of the parallelogram.