Question

In $△$ $PQR$, $S$ and $T$ are two points on $PQ$ and $PR$ respectively, such that $PS=4$ cm, $SQ=3$ cm, $PT=6$ cm, $TR=4.5$ cm and $\angle PST={40}^o$. Find $\angle PQR$.

Answer 1

In $△PQR$, we have

$\frac{PS}{SQ}=\frac{4}{3}$

$\frac{PT}{TR}=\frac{6}{4.5}=\frac{4}{3}$

$\frac{PS}{SQ}=\frac{PT}{TR}\therefore ST||QR$ ($\because$ Converse of Thales theorem)

Therefore, $\angle PST=\angle PQR={40}^o$ ($\because$ Corresponding angles)