Correct Answer: $80^{\circ},65^{\circ},$ and $35^{\circ}$

Solution : Given that $\angle A - \angle B = 15^{\circ}$ and $\angle B - \angle C = 30^{\circ}$.
$\angle A = \angle B + 15^{\circ}$
$\angle C = \angle B - 30^{\circ}$
We know that the sum of the angles in a triangle is $180^{\circ}$.
$\angle A + \angle B + \angle C = 180^{\circ}$
Substituting the expressions for $\angle A$ and $\angle C$.
$(\angle B + 15^{\circ}) + \angle B + (\angle B - 30^{\circ}) = 180^{\circ}$
⇒ $3\angle B - 15^{\circ} = 180^{\circ}$
⇒ $3\angle B = 195^{\circ}$
⇒ $\angle B = 65^{\circ}$
Substituting $\angle B = 65^{\circ}$ into the expressions for $\angle A$ and $\angle C$,
$\angle A = 65^{\circ} + 15^{\circ} = 80^{\circ}$
$\angle C = 65^{\circ} - 30^{\circ} = 35^{\circ}$
Hence, the correct answer is $80^{\circ}$, $65^{\circ}$, and $35^{\circ}$.