Question

Find the $\angle x$ in the given figure, if AB || CD.​

• A. ${75}^{\circ }$
• B. ${55}^{\circ }$
• C. ${160}^{\circ }$
• D. ${145}^{\circ }$

Answer 1

The correct option is D ${145}^{\circ }$

​
Draw PQ || AB and CD​

$x=\angle CPQ+\angle BPQ$

$\angle BPQ=\angle ABP=20°$(alternate interior angles)​

$\angle CPQ+\angle DCP=180°$(co-interior angles are supplementary)​

$\angle CPQ+55°=180°$

$\angle CPQ=180°-55°=125°$

Therefore, ​

$x=\angle CPQ+\angle BPQ$

$=20°+125°$

$=145°$

​Answer: (D) 145°​