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Question
In the given figure, if lines l and m are parallel lines, then x =
Options
70°
100°
40°
30°
Solution
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 \[40^\circ\]
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