question_answer

If CE is parallel to DB in the given figure, then value of x will be ________.

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

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

C) \[30{}^\circ \]                          

D) \[85{}^\circ \]

E) None of these

Correct Answer: D

Solution :

Explanation \[\angle ADB = 180{}^\circ  - \left( 110{}^\circ  + 30{}^\circ  \right) = 40{}^\circ \] \[\angle BDC=75{}^\circ -40{}^\circ =35{}^\circ \] \[\operatorname{DB} \parallel  CE\] \[\therefore \,\,\, 35{}^\circ  + \left( 60{}^\circ  + x{}^\circ  \right) = 180{}^\circ \] \[\Rightarrow \,\,\,\,x=85{}^\circ .\]