Question

In the given figure if $PQ||RS$. then the measure of $m$ is :

• A. ${110}^{\circ }$
• B. ${100}^{\circ }$
• C. ${90}^{\circ }$
• D. ${137}^{\circ }$

Answer 1

The correct option is A ${110}^{\circ }$

$PQ||RS$ and $PS$ is transversal .

$\therefore \angle QPS=\angle PSR$ (Alternate angles)

$\Rightarrow \angle PSR={43}^{\circ }$

Now in the lower triangle by using angle sum property of triangle

$m+{43}^{\circ }+{27}^{\circ }={180}^{\circ }\Rightarrow m+{70}^{\circ }={180}^{\circ }\Rightarrow m={180}^{\circ }-{70}^{\circ }={110}^{\circ }$