Answer
$\angle A=62^{\circ}$
$a\approx199.55$
$b\approx241.52$
Work Step by Step
$\angle {A}+ \angle {B}+\angle {C}=180^{\circ}$
$\implies \angle C=180^{\circ}-\angle {A}-\angle {B}$
$=180^{\circ}-50^{\circ}-68^{\circ}=62^{\circ}$
From the law of sines, we have
$\frac{\sin C}{c}=\frac{\sin A}{a}$
$\implies a\sin C=c\sin A$
Or $a=c\cdot \frac{\sin A}{\sin C}=230\times\frac{\sin 50^{\circ}}{\sin 62^{\circ}}$
$a\approx 199.55$
Similarly,
$\frac{\sin C}{c}=\frac{\sin B}{b}$
$\implies b=c\cdot \frac{\sin B}{\sin C}$
$=230\times\frac{\sin 68^{\circ}}{\sin62^{\circ}}\approx241.52$