Question

In the given figure, it is given that line ABDE is a straight line and AE || PQ . FInd $\angle$PCB and $\angle$QCD.

• A. ${110}^{\circ }$, ${100}^{\circ }$
• B. ${60}^{\circ }$, ${30}^{\circ }$
• C. ${70}^{\circ }$, ${80}^{\circ }$
• D. ${45}^{\circ }$, ${45}^{\circ }$

Answer 1

The correct option is C ${70}^{\circ }$, ${80}^{\circ }$

As, AE || PQ, we have
$\angle$PCB + $\angle$ABC = ${180}^{\circ }$
[$\because$co-interior angles]
or, $\angle$PCB + ${110}^{\circ }$ = ${180}^{\circ }$
i.e, $\angle$PCB = ${70}^{\circ }$

Similarly, $\angle$QCD = ${80}^{\circ }$