#### Question

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

#### Solution

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°

Is there an error in this question or solution?

Solution In the Adjoining Figure, Line P || Line L || Line Q. Find ∠X with the Help of the Measures Given in the Figure. Concept: Properties of Angles Formed by Two Parallel Lines and a Transversal.