question_answer

In the given figure, \[\mathbf{AB}\parallel \mathbf{CD}\]. Then what is the value of x?

A)  \[{{140}^{{}^\circ }}\]          

B)  \[{{45}^{{}^\circ }}\]           

C)  \[{{120}^{{}^\circ }}\]                                  

D)  \[{{75}^{{}^\circ }}\]

Correct Answer: A

Solution :

(a): Draw EF parallel to both. AB and CD. Now, AB I; EF and transversal AR cuts them w k and E respectively. \[\angle BAE+\angle FEA={{180}^{{}^\circ }}\] \[\Rightarrow \]\[{{108}^{{}^\circ }}\angle 1={{180}^{{}^\circ }}\] \[\Rightarrow \] \[\angle 1={{180}^{{}^\circ }}-{{108}^{{}^\circ }}={{72}^{{}^\circ }}\] Again, \[EF\parallel CD\] and transversal CE cuts them at E and F respectively. \[\angle FEC+\angle ECD={{180}^{{}^\circ }}\] \[\Rightarrow \]   \[\angle 2+{{112}^{{}^\circ }}={{180}^{{}^\circ }}\] \[\Rightarrow \]  \[\angle 2={{180}^{{}^\circ }}-{{112}^{{}^\circ }}\] \[\Rightarrow \]   \[\angle 2={{68}^{{}^\circ }}\] Now,     \[x=\angle 1+\angle 2\] \[\Rightarrow \] \[x={{72}^{{}^\circ }}+{{68}^{{}^\circ }}={{140}^{{}^\circ }}\]