Question

If $LO||MN$, find the value of $p$.

• A. ${50}^{\circ }$
• B. ${46}^{\circ }$
• C. ${56}^{\circ }$
• D. ${52}^{\circ }$

Answer 1

The correct option is C ${56}^{\circ }$

Here $△LMN$ is right angle triangle.
And $\angle NLM+\angle LMN+\angle MNL={180}^o$ .....[Angle sum property]
${59}^o+{90}^o+\angle MNL={180}^o$
$\angle MNL={180}^o-{149}^o={31}^o$.

Given, $\angle LNO={25}^o$.
So, $\angle MNO=\angle MNL+\angle LNO={31}^o+{25}^o={56}^o$.
As $LO || MN$and$ON6$ is crossing both the lines so,
$\angle MNO=\angle p={56}^o$ ....[Alternate Interior angles]

Hence, option $C$ is correct.