question_answer

In the figure given below, \[AB\parallel CD\] and EF intersects them. Then, the value of x is

A) \[18{}^\circ \]                          

B) \[14{}^\circ \]

C) \[28{}^\circ \]  

D) \[24{}^\circ \]

Correct Answer: C

Solution :

According to the question,

From figure, \[\angle EOB=\angle EMD=2x{}^\circ \]

[corresponding angel]

Now,\[\angle EMD+\angle EMC=180{}^\circ \]

\[\therefore \]      \[4x+12{}^\circ +2x=180{}^\circ \]

\[\Rightarrow \]   \[6x+12{}^\circ =180{}^\circ \]\[\Rightarrow \]\[6x=168{}^\circ \]

\[\Rightarrow \]   \[x=\frac{168{}^\circ }{6}\]\[\Rightarrow \]\[x=28{}^\circ \]