question_answer

In the following figure, if AX is parallel to CY, then find x.

A) \[130{}^\circ \]

B) \[170{}^\circ \]

C) \[190{}^\circ \]            

D) \[180{}^\circ \]

E) None of these

Correct Answer: A

Solution :

Explanation Extend AB and YC as shown so that they meet in P. In \[\Delta \,BCP\] \[\begin{align}  & \angle \,BCP = 180{}^\circ  - 120{}^\circ  = 60{}^\circ \,\,\,\,\,(\therefore \,\,PCY\,\,is\,\,a\,\,straight\,\,line) \\  & \angle  \\ \end{align}\]\[\angle \,BPC=180{}^\circ -110{}^\circ =70{}^\circ \] (\[\therefore \text{ }\,\,\angle \,BAX\text{ }and\text{ }\angle BPY\] are the interior angles of two parallel lines AX and CY) \[\therefore \,\,\,x = \angle BCP + \angle BPC = 60{}^\circ  + 70{}^\circ  = 130{}^\circ \]