question_answer

ABCD is a parallelogram in which \[\angle BCD\] and \[{{75}^{o}}\]then \[{{105}^{o}}\]

A)  \[{{85}^{o}}\]                                

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

C)  \[\angle BAC={{45}^{o}}\]     

D)  \[\angle BED={{120}^{o}}\]

Correct Answer: C

Solution :

We have, \[{{65}^{o}}\]   (\[{{105}^{o}}\] \[{{95}^{o}}\]) In  \[{{85}^{o}}\] \[\angle A={{60}^{o}},\] \[CE||BA\]      \[\angle ECD={{65}^{o}}\] \[\angle ACB=\]          \[{{60}^{o}}\] \[{{55}^{o}}\]          \[{{70}^{o}}\] (Alternate interior angles)