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.

$x=\angle CPQ+\angle BPQ$
$\angle BPQ={20}^{\circ }[\because \text{alternate interiior angles}]$
$\angle CPQ+{55}^{\circ }={180}^{\circ }[\because \text{sum of co-interior angles is 180}]$

From the figure and the above statements
$x={20}^{\circ }+({180}^{\circ }-{55}^{\circ })$
$x={20}^{\circ }+{125}^{\circ }={145}^{\circ }$