Question

In the given figure, sides QP and RQ of a triangle PQR are produced to the points S and T respectively. If $\angle SPR={135}^o$ and $\angle PQT={110}^o$, find $\angle PRQ$.

Answer 1

Since Q, P and S all lie on the same line,
$angleQPR+\angle SPR={180}^o$.
Hence, $\angle QPR+{135}^o={180}^o$
or $\angle QPR={180}^o-{135}^o={45}^o$.
Using exterior angle property in triangle PQR, we have
$\angle PQT=\angle QPR+\angle PRQ.$
This gives ${110}^o={45}^o+\angle PRQ$
Solving for $\angle PRQ,$ we get $\angle PRQ={110}^o-{45}^o={65}^o$.