Question

Mark (✓) against the correct answer
In the given figure, AB || CD. ∠OAB = 150° and ∠OCD = 120°.
Then ∠AOC = ?



(a) 80°
(b) 90°
(c) 70°
(d) 100°

Answer 1

$$\begin{gathered} \left(b\right)90° \\ \begin{array}{l}\text{Draw a parallel line through O and produce AB and CD on R and P, respectively}\text{.}\\ \\ \therefore \angle \text{OCD}=\angle {\text{COQ=120}}^0\text{(alternate angles)}\end{array} \\ \angle {\text{COS=180}}^0-{120}^0(\mathrm{linear}\mathrm{pair}) \\ ={60}^0 \\ \text{Similarly,}\angle \text{AOQ=}\angle {\text{BAO=150}}^0(alternate\; angles) \\ \angle {\text{AOS=180}}^o-{150}^0(\mathrm{linear}\mathrm{pair}) \\ ={30}^0 \\ \angle AOC=\angle AOS+\angle COS \\ \therefore \angle {\text{AOC=60}}^0+{30}^0={90}^0 \end{gathered}$$