In Fig. PQ || RT. Find the value of a + b. - Vidyadip

Question

In Fig. $PQ || RT.$ Find the value of $a + b.$

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Answer

Since, $PQ || RT$ and $RQ$ is transversal.
Therfore, $\angle\text{TQR}=\angle\text{RQP}$ [Alternate interior angles]
$\Rightarrow\text{b} =55^\circ$
Also, $\angle\text{SRT}=\angle\text{SPQ}$ [Corresponding angles]
$\Rightarrow\text{a} =45^\circ$
$\therefore \text{a}+\text{b}+45^\circ+55^\circ=100^\circ$

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