Question

In the given figure, AB||CD. If $\angle AOC={30}^{\circ }$ and $\angle OAB={100}^{\circ }$ then $\angle OCD=?$

$\left(a\right){130}^{\circ }$

$\left(b\right){150}^{\circ }$

$\left(c\right){80}^{\circ }$

$\left(d\right){100}^{\circ }$

Answer 1

Draw OE ∥ AB ∥ CD.
Now, OE ∥ AB and OA is the transversal.
∴∠OAB+∠AOE=180° Angles on the same side of a transversal line are supplementary
⇒∠OAB+∠AOC+∠COE=180°
⇒100°+30°+∠COE=180°
⇒∠COE=50°

Also, OE ∥ CD and OC is the transversal.
∴∠OCD+∠COE=180° (Angles on the same side of a transversal line are supplementary)
⇒∠OCD+50°=180°
⇒∠OCD=130°

So, option (a) is coprrect.