Question

In figure, if $QP\parallel SR$, the value of $a$ is

• A. ${40}^o$
• B. ${30}^o$
• C. ${90}^o$
• D. ${80}^o$

Answer 1

The correct option is C ${90}^o$

Option (c) is correct.

We will construct $LM$ such that $LM||PQ||SR$

Here, $LM$ parallel to $QP$ and $QT$ is a transversal.

$\therefore \angle LTQ=\angle PQT\cdots \cdots [\because \text{alternate angles}]$

$\Rightarrow \angle LTQ={60}^0$ ....(1)

Also, $LM$ parallel to $SR$ and $TS$ is a transversal.

$\therefore \angle TSR=\angle LTS\cdots \cdots [\because \text{alternate angles}]$

$\Rightarrow \angle LTS={30}^0$ ....(2)

From equation 1 and 2, we get

$a=\angle LTQ+\angle LTS={60}^0+{30}^0={90}^0$