Answer
$ \angle B=85^{\circ}$
$a=5$
and
$c=9.1$
Work Step by Step
I. Need to find the last angle.
$30^{\circ}+\angle B+65^{\circ}=180^{\circ}$
$\implies \angle B=85^{\circ}$
II. Use law of sines formula to find $a$ and $b$
$\dfrac{\sin 30^{\circ}}{a}=\dfrac{\sin 85^{\circ} }{10}=\dfrac{\sin 65^{\circ} }{c}$
This implies that
$a=\dfrac{10 \sin 30^{\circ} }{\sin 85^{\circ}}=5$
and
$c=\dfrac{10 \sin 65^{\circ} }{\sin 85^{\circ}}=9.1$
