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.
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Let two adjacent angles A and B of ∥gm ABCD be 3x and 2x respectively.
Since the adjacent angles of a parallelogram are supplementary.
∠A+∠B=180
⇒3x+2x=180o
⇒5x=180
⇒x=5180o=36
∴∠3×36o=108o
and, ∠B=2×36o=72o
Since the opposite angles are equal in a parallelgram, therefore,
∠C=∠A=108o and ∠D=∠B=72o
Hence, ∠A=108o,∠B=72o,∠C=108o and ∠D=72o
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