question_answer

If AY parallel to CX, then find \[\angle \]ABC.

A) \[45{}^\circ \]                          

B) \[60{}^\circ \]

C) \[75{}^\circ \]                          

D) \[90{}^\circ \]

E) None of these

Correct Answer: B

Solution :

Explanation \[\angle \,CEZ\,=\,\,50{}^\circ \] \[\angle CEZ = \angle AEB = 50{}^\circ \](Vertically opposite angles) and \[\angle \,YAB + \angle BAE = 180{}^\circ \] (Linear pair) \[\angle BAE = 70{}^\circ \] \[\Rightarrow \,\,\operatorname{ABC} = 180{}^\circ  - \left( 70{}^\circ  + 50{}^\circ  \right) = 180{}^\circ  - 120{}^\circ  = 60{}^\circ .\]