question_answer

In the given figure, \[\mathbf{AB}\parallel \mathbf{CD},\angle \mathbf{ABE}={{95}^{{}^\circ }}\], Find \[\angle \mathbf{CDE}\]:

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

B)  \[{{110}^{{}^\circ }}\]

C)  \[{{125}^{{}^\circ }}\]      

D)  \[{{100}^{{}^\circ }}\]

Correct Answer: C

Solution :

(c): Extend CD to M then \[\angle DME=\angle ABC={{95}^{{}^\circ }}\] \[\angle MED={{30}^{{}^\circ }}\] \[\therefore \]\[\angle MDE={{180}^{{}^\circ }}-\left( {{95}^{{}^\circ }}+{{30}^{{}^\circ }} \right)={{55}^{{}^\circ }}\] \[\therefore \]\[\angle CDE={{180}^{{}^\circ }}-{{55}^{{}^\circ }}={{125}^{{}^\circ }}\]