Question

In the diagram above, if $PQ$ and $CD$ are parallel to each other and $\angle 1={60}^{\circ }$, then $\angle 6=$.

• A. ${60}^{\circ }$
• B. ${120}^{\circ }$
• C. ${150}^{\circ }$

Answer 1

The correct option is B ${120}^{\circ }$

For the diagram given:
$\angle 1={60}^{\circ }$, and $CD$ are prallel to $PQ$.
Now, $\angle 1$ and $\angle 3$ are vertically opposite angles.
$\Rightarrow \angle 1=\angle 3={60}^{\circ }$.
Now $\angle 3$ and $\angle 6$ are a pair of co-interior angles.
$\Rightarrow \angle 3+\angle 6={180}^{\circ }$
$\Rightarrow \angle 6+{60}^{\circ }={180}^{\circ }$
$\Rightarrow \angle 6={180}^{\circ }-{60}^{\circ }={120}^{\circ }$
$\therefore \angle 6={120}^{\circ }$