Question

In fig, side QR of $\Delta PQR$ has been produced to S. If $\angle P:\angle Q:\angle R=3:2:1$ and RT is perpendicular to PR. Find $\angle TRS$.

Answer 1

In $\Delta PQR$

$\Rightarrow \angle P+\angle Q+\angle R={180}^{\circ }$ (Angle sum property)

$\angle P:\angle Q:\angle R=3:2:1$ (Given)

Sum of the ratios = 3 + 2 + 1 = 6

$\Rightarrow \angle PRQ=\frac{1}{6}\times {180}^{\circ }$

$\Rightarrow \angle PRQ={30}^{\circ }$

$\Rightarrow \angle PRQ+\angle PRT+\angle TRS={180}^{\circ }$ (Sum of the angles are supplementary)

$\Rightarrow {30}^{\circ }+{90}^{\circ }+\angle TRS={180}^{\circ }$

$\Rightarrow \angle TRS={180}^{\circ }-{120}^{\circ }$

$\Rightarrow \angle TRS={60}^{\circ }$