Question

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

Options

• 70°

• 100°

• 40°

• 30°

Answer 1

We have the following figure:

It is given that l || m

We know that consecutive interior angles are supplementary.

Therefore,

∠1 + 70° = 180°

∠1 = 180° - 70°

∠1 = 110°                (1)

\[\angle1 = \angle AOB = 110 (\text { vertically opposite angles })\]

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

In ΔAOB:

\[30^\circ+ x + 110^\circ= 180^\circ\]

\[ \Rightarrow x = 180 - 110 - 30 = 40\]

Hence, the value of x will be \[40^\circ\]