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°