question_answer

In the figure below, if \[\left. AB \right\|CD\] and CE \[\bot \] ED, then the value of \[x\]is

A)  53                               

B)  63

C)  37                               

D)  45

Correct Answer: A

Solution :

\[\angle\]AEC + \[\angle\]CAD +\[\angle\]DEB = \[{{180}^{{}^\circ }}\] \[\Rightarrow\]  \[{{37}^{{}^\circ }}+{{90}^{{}^\circ }}\] + \[\angle\]DEB = \[{{180}^{{}^\circ }}\] \[\Rightarrow\] \[\angle\] DEB = \[180{}^\circ\] - \[127{}^\circ \] = \[53{}^\circ \] \[EB\text{  }\!\!|\!\!\text{  }\!\!|\!\!\text{  }CD\] \[\therefore\] \[\angle\]BED =\[\angle\]EDC = \[53{}^\circ \]