Question

In the adjoining figure, line p II line l II line q. Find $\angle x$ with the help of the measures given in the figure.

• A. ${50}^o$
• B. ${60}^o$
• C. ${65}^o$
• D. ${70}^o$

Answer 1

The correct option is D ${70}^o$

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 $\angle LMD=\angle ALM$ (Alternate interior angles)
$\Rightarrow \angle LMD={40}^o$
Since, CD||PQ and MN is a transversal intersecting CD at M and PQ at N, then $\angle DMN={30}^o$
Now, $\angle LMD+\angle DMN={40}^o+{30}^o$
$\Rightarrow \angle LMN={70}^o$
$\Rightarrow x={70}^o$