Question

In the figure, PQ || RS, TR|| QU and $\angle PTR={42}^{\circ }$. Then $\angle QUR$ is equal to:

• A. ${148}^{\circ }$
• B. ${138}^{\circ }$
• C. ${38}^{\circ }$
• D. ${128}^{\circ }$

Answer 1

The correct option is B ${138}^{\circ }$

Since PQ||RS and TR is a transversal,
$\angle PTR=\angle TRS$ (Alternate interior angles are equal)
Or $\angle TRS={42}^{\circ }$
Now TR||QU and RS is a transversal.
$\therefore \angle TRS+\angle QUR={180}^{\circ }$ (Angles on the same side of a transversal are supplementary)
Or, ${42}^{\circ }+\angle QUR={180}^{\circ }$
$\angle QUR={180}^{\circ }-{42}^{\circ }={138}^{\circ }$