Question

In the adjoining figure, if line a || line b and line l is a transversal then find x. 

पर्याय

• 90°

• 60°

• 45°

• 30°

Answer 1

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°