7. In the triangle $P Q R$, the lengths of sides $P Q$ and $P R$ are the same. The point $S$ lies on $Q R$ so that $Q S=P S$ and $\angle R P S=75^{\circ}$. What is the size of $\angle Q R P$ ?
A $35^{\circ}$
B $30^{\circ}$
C $25^{\circ}$
D $20^{\circ}$
E $15^{\circ}$
7. A Let $\angle P Q S$ be $x^{\circ}$. Since $P Q=P R$, the triangle $P Q R$ is isosceles and hence $\angle Q R P=x^{\circ}$. Also, since $Q S=P S$, the triangle $P Q S$ is isosceles and hence $\angle S P Q=x^{\circ}$. Therefore, since angles in a triangle add to $180^{\circ}$, we have $x+x+x+75=180$, which has solution $x=35$. Hence the size of $\angle Q R P$ is $35^{\circ}$.