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.

$x=\angle CPQ+\angle BPQ$

$\angle BPQ={20}^{\circ }[\because \text{alternate interior angles}]$

$\angle CPQ+{55}^{\circ }={180}^{\circ }[\because \text{sum of co-interior angles is 180}]$

$\angle CPQ={180}^{\circ }-{55}^{\circ }$

$x={20}^{\circ }+({180}^{\circ }-{55}^{\circ })$

$x={20}^{\circ }+{125}^{\circ }={145}^{\circ }$