Solve for the variables in each of the diagrams?

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1 Answer
Aug 2, 2017
  1. x=6 cm.
  2. a=70, b=c=55

Explanation:

Ques.No.1
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In DeltasABO and COD

/_AOB=/_COD - vertically opposite angles
/_ABO=/_DCO - alternate opposite angles as AB||CD
/_BAO=/_ODC - alternate opposite angles as AB||CD

As such DeltasABO and COD are similar and hence

(CO)/(OB)=(CD)/(AB) i.e. x/2=12/4

and x=12/4xx2=6 cm.

Ques.No.2
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As AB||CE and AC is transverse /_a=70^@ as they are alternate interior angles.

Further as AB||CE and BC is transverse /_b=/_c as they are corresponding angles.

Now in DeltaABC, we have AB=AC, hence /_ACB=/_ABC=b^@

Hence 2b^@+a^@=2b^@+70^@=180^@

or 2b^@=180^@-70^@=110^@ i.e. b=55

and as /_c=/_b=55^@, c=55