Question

In fig. 1 $PQ||RS,\angle QPR={70}^{\circ },\angle ROT={20}^{\circ }$; find the value of $x$.

• A. ${20}^{\circ }$
• B. ${70}^{\circ }$
• C. ${110}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

Answer: (D)

${50}^{\circ }$

$PQ||RS$ and $PO$ is transversal

$\therefore \angle SRO=\angle QPR$ (Corresponding angles)

$\Rightarrow \angle SRO={70}^{\circ }$

We we know exterior angle of triangle is equal to sum of interior opposite angles.

Applying this in $△TRO$

$\Rightarrow \angle RTO+\angle ROT=\angle SRO$

$\Rightarrow x+{20}^{\circ }={70}^{\circ }\Rightarrow x={70}^{\circ }-{20}^{\circ }={50}^{\circ }$