Question

In the figure (not drawn to scale), $AB$ is parallel to $CD$ and $\angle ECD$ is a right angle. Find $\angle y$.

• A. ${111}^{\circ }$
• B. ${112}^{\circ }$
• C. ${113}^{\circ }$
• D. ${114}^{\circ }$

Answer 1

Answer: (B)

${112}^{\circ }$

Since, $AB\parallel CD$

$\therefore \angle CAB+\angle DCA={180}^{\circ }$ (Co-interior angles)

$\therefore {22}^{\circ }+\angle DCA={180}^{\circ }$

$\Rightarrow \angle DCA={180}^{\circ }-{22}^{\circ }={158}^{\circ }$

Also, $\angle ECD+\angle DCA+\angle y={360}^{\circ }$ (Angles about a point)

$\Rightarrow {90}^{\circ }+{158}^{\circ }+\angle y={360}^{\circ }$

$\Rightarrow \angle y={360}^{\circ }-({90}^{\circ }+{158}^{\circ })$

$\Rightarrow y={360}^{\circ }-{248}^{\circ }={112}^{\circ }$.