Question

In the given figure, if MN $\parallel$ PQ, then find the value of $x$.

• A. ${75}^o$
• B. ${65}^o$
• C. ${35}^o$
• D. ${140}^o$

Answer 1

The correct option is A ${75}^o$

Given that, MN $\parallel$ PQ
$\angle NRO={140}^0,\angle PSO={35}^0$
Now,draw the line VW parallel to PQ and passong through point 'O'.


$\angle ROW+\angle SOW=\angle ROS$
$\angle ORN+\angle ROS={180}^o$ [co-interior angles]
$\Rightarrow \angle ROS=180-140={40}^o$
and $\angle PSO=\angle WOS$ [Alternate interior angles]
$\Rightarrow \angle WOS={35}^o$
$\because \angle ROW+\angle SOW=\angle ROS\Rightarrow x={40}^o+{35}^o={75}^o$