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Question
In the adjoining figure, if line a || line b and line l is a transversal then find x.
Options
90°
60°
45°
30°
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Solution
30°
Explanation:
Let us mark the points P and Q on a; R and S on b; A and B on l.
Suppose PQ and AB intersect at M; RS and AB intersect at N.
Since a||b and l is a transversal, then
m∠ RNM = m∠ SNB (Vertically opposite angles)
⇒ ∠ RNM = 2x
Now, m∠ RNM + m∠ PMN = 180° (Interior angles on the same side of the transversal are supplementary)
⇒ 2x + 4x = 180°
⇒ 6x = 180°
⇒ x = `(180°)/6`
⇒ x = 30°
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