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
1. 108°, 52°
2. 112°, 68°
3. 108°,72°
4. 120°,60°
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Answer:
3. 108°,72°
Step-by-step explanation:
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
o
⇒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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