Question

Choose the correct alternative. 

In the adjoining figure, if line m || line n and line p is a transversal then find x. 

Options

• 135°

• 90°

• 45°

• 40°

Answer 1

Let us mark the points 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 is a transversal, then
m∠QMN + m∠SNM = 180°    (Interior angles on the same side of transversal are supplementary)
Substituing the values in the above equation, we get
3x + x = 180°
⇒ 4x = 180°
⇒ x = `(180°)/4`
∴ x = 45°
So, the correct answer is option (C).