Question

In the given figure, AB||CD. If $\angle APQ={70}^{\circ }$ and $\angle PRD={120}^{\circ }$ then $\angle QPR=?$

$\left(a\right){50}^{\circ }$

$\left(b\right){60}^{\circ }$

$\left(c\right){40}^{\circ }$

$\left(d\right){35}^{\circ }$

Answer 1

ANSWER:
$\left(a\right){50}^{\circ }$
AB∥CD and PQ is the transversal.
∴ $\angle PQR=\angle APQ={70}^{\circ }$ Alternate Interior Angles
Side QR of traingle PQR is produced to D.
∴ $\angle PQR+\angle QPR=\angle PRD\Rightarrow {70}^{\circ }+\angle QPR={120}^{\circ }\Rightarrow \angle QPR={50}^{\circ }$