question_answer

In the given figure, if \[l||m,\]then find the value of x.

A) \[105{}^\circ \]

B) \[100{}^\circ \]

C) \[110{}^\circ \]            

D) \[115{}^\circ \]

E) None of these

Correct Answer: A

Solution :

Draw a line n passing through O and parallel to l and m.

Since,\[l||n,\]     \[\angle 1+100{}^\circ =180{}^\circ \]

[sum of the interior angles on the same side of the transversal]

\[\Rightarrow \]               \[\angle 1=80{}^\circ \]

Since, \[n||m,\]\[\angle 2=30{}^\circ \]   [alternate angles]

Now, \[AOB=\angle 1+\angle 2\]

\[=\,\,(80+30{}^\circ )=110{}^\circ \]

But       \[\angle AOB=(X+5){}^\circ =110{}^\circ \]

\[\Rightarrow \]\[x=(110-5){}^\circ =105{}^\circ \]