sat-dog

Choice B is correct. It's given that quadrilateral $P^{\text{'}}{Q}^{\text{'}}{R}^{\text{'}}{S}^{\text{'}}$ is similar to quadrilateral $PQRS$, where $P$, $Q$, $R$, and $S$ correspond to $P^{\text{'}}$, $Q^{\text{'}}$, $R^{\text{'}}$, and $S^{\text{'}}$, respectively. Since corresponding angles of similar quadrilaterals are congruent, it follows that the measure of angle $P$ is equal to the measure of angle $P^{\text{'}}$. It's given that the measure of angle $P$ is $30°$. Therefore, the measure of angle $P^{\text{'}}$ is $30°$.

Choice A is incorrect. This is $\frac{1}{3}$ the measure of angle $P^{\text{'}}$.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is $3$ times the measure of angle $P^{\text{'}}$.