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.
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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
o
⇒3x+2x=180
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⇒5x=180
o
⇒x=
5
180
o
=36
o
∴∠3×36
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=108
o
and, ∠B=2×36
o
=72
o
Since the opposite angles are equal in a parallelgram, therefore, ∠C=∠A=108
o
and ∠D=∠B=72
o
Hence, ∠A=108
o
,∠B=72
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,∠C=108
o
and ∠D=72
o
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