Question

In the adjoining figure, AB is parallel to CD. Find the value of x.

• A. 80${}^{\circ }$
• B. 88${}^{\circ }$
• C. 90${}^{\circ }$
• D. 98${}^{\circ }$

Answer 1

The correct option is D

98${}^{\circ }$

Draw a line parallel to AB and CD passing through O.

Now we know that interior angles on the same side of the transversal are supplementary

Therefore $\angle$BAO + $\angle$AOR = 180${}^{\circ }$

⇒ $\angle$AOR + 130${}^{\circ }$ = 180${}^{\circ }$

⇒ $\angle$AOR = 50${}^{\circ }$

and similarly

$\angle$ROC + $\angle$OCD = 180${}^{\circ }$

⇒ $\angle$ROC + 132${}^{\circ }$ = 180${}^{\circ }$

⇒ $\angle$ROC = 48${}^{\circ }$

Hence

$\angle$AOC = 50${}^{\circ }$ + 48${}^{\circ }$

⇒ $\angle$AOC = 98${}^{\circ }$