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Question

Two adjacent angles of a parallelogram are (3x4) and (3x+10). Find the angles of the parallelogram.
  1. A=83,B=97,C=83,D=97
  2. A=83,B=83,C=97,D=97
  3. A=97,B=83,C=97,D=83
  4. A=78,B=89,C=78,D=89


Solution

The correct option is A A=83,B=97,C=83,D=97

Let in parallelogram ABCD,
A=3x4and B=3x+10

AD || BC and AB is a transversal.
Then, A+B=180
(Interior angles of same side of the transversal is supplementary)

(3x4)+(3x+10)=1806x+6=1806x=1806=174x=1746=29A=3x4=3×294=874=83
B=(3x+10)=3×29+10=87+10=97

But C=A and D=B
(Opposite angles of a parallelogram are equal)
C=83and D=97
Hence, A=83,B=97,C=83 and D=97. 
 

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