Question

In fig. TQ and TR are bisectors of $\angle$Q and $\angle$R respectively. If $\angle$QPR = ${80}^{\circ }$ and $\angle$PRT = ${30}^{\circ }$. Determine $\angle$TQR. [4 MARKS]

Answer 1

Since the bisectors of $\angle$Q and $\angle$R meet at T.

$\angle$QTR = ${90}^{\circ }$ + $\frac{1}{2}$$\angle$QPR [By Corollary] (1 Mark)

$\Rightarrow$ = ${90}^{\circ }$ + $\frac{1}{2}\times {80}^{\circ }$

$\Rightarrow \angle$QTR = ${130}^{\circ }$ (1 Mark)

In $\Delta$QTR, we have

$\angle$TQR + $\angle$QTR + $\angle$TRQ = ${180}^{\circ }$

$\Rightarrow$ $\angle$TQR + ${130}^{\circ }$ + ${30}^{\circ }$ = ${180}^{\circ }$ (1 Mark)

$\Rightarrow$ $\angle$TQR = ${20}^{\circ }$ (1 Mark)