Question

In the given figure, if lines l and m are parallel lines, then x =

(a) 70°

(b) 100°

(c) 40°

(d) 30°

Answer 1

We have the following figure:

It is given that

We know that consecutive interior angles are supplementary.

Therefore,

$\angle 1=\angle AOB=110(\mathrm{vertically}\mathrm{opposite}\mathrm{angles})$

In a triangle, we know that, the sum of the angles is supplementary.

In ΔAOB:

$$\begin{gathered} 30°+x+110°=180° \\ \Rightarrow x=180-110-30=40 \end{gathered}$$

Hence, the value of x will be $40°$.
Thus, (c) is the correct answer.