In the diagram, $P Q R S$ is a square and $P T Q$ is an equilateral triangle. What is the measure of $\angle T P R$ ?
(A) $90^{\circ}$
(B) $105^{\circ}$
(C) $120^{\circ}$
(D) $150^{\circ}$
(E) $75^{\circ}$

![](https://cdn.mathpix.com/cropped/2024_04_20_ac36362783317e0251fdg-062.jpg?height=418&width=307&top_left_y=1382&top_left_x=1275)
Each interior angle in a square is $90^{\circ}$. In particular, $\angle S P Q=90^{\circ}$.

Each interior angle in an equilateral triangle is $60^{\circ}$. In particular, $\angle T P Q=60^{\circ}$.

$P R$ is a diagonal of square $P Q R S$. Thus, it bisects angle $\angle S P Q$, with $\angle S P R=\angle R P Q=45^{\circ}$. Therefore, $\angle T P R=\angle T P Q+\angle Q P R=60^{\circ}+45^{\circ}=105^{\circ}$.

ANSWER: (B)