Question

In the adjoining figure, line p ∥ line l ∥ line q. Find ∠x with the help of the measures given in the figure.

Answer 1

Let us mark the points A, L and B on p; C, M and D on l; P, N and Q on q.
Since, AB||CD and LM is a transversal intersecting AB at L and CD at M, then
m∠LMD = ​m∠ALM (Alternate interior angles)
⇒ m∠LMD = 40°
Since, CD||PQ and MN is a transversal intersecting CD at M and PQ at N, then
m∠DMN = ​m∠PNM (Alternate interior angles)
⇒ m∠DMN = 30°
Now, m∠LMD + m∠DMN = 40° + 30°
⇒ m∠LMN = 70°
⇒ x = 70°