Question

In the adjoining figure, it is given that AB || CD, $\angle$BAO = 108${}^{\circ }$ and $\angle$OCD = 120${}^{\circ }$ then $\angle$AOC = ________.

• A. 120${}^{\circ }$
• B. 72${}^{\circ }$
• C. 132${}^{\circ }$
• D. 150${}^{\circ }$

Answer 1

The correct option is C

132${}^{\circ }$

Let us redraw the given figure as follows:

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

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

⇒ $\angle$AOR = 72${}^{\circ }$

and similarly

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

⇒ $\angle$ROC + 120${}^{\circ }$ = 180${}^{\circ }$

⇒ $\angle$ROC = 60${}^{\circ }$

Hence

$\angle$AOC = 60${}^{\circ }$ + 72${}^{\circ }$

⇒ $\angle$AOC = 132${}^{\circ }$