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Question
In the adjoining figure, if line m || line n and line p are a transversal then find x.
Options
135°
90°
45°
40°
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Solution
45°
Explanation:
Let us mark P and Q on m, R, and S on n, A, and B on p.
Suppose PQ and AB intersect at M; RS and AB intersect at N.
Since, m||n and p are transversals, then
m∠QMN + m∠SNM = 180° (Interior angles on the same side of transversal are supplementary)
Substituting the values in the above equation, we get
3x + x = 180°
⇒ 4x = 180°
⇒ x = `(180°)/4`
∴ x = 45°
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