10. A square has vertices $P, Q, R, S$ labelled clockwise. An equilateral triangle is constructed with vertices $P, T, R$ labelled clockwise. What is the size of angle $R Q T$ in degrees?
A 30
B 45
C 135
D 145
E 150
10. C The diagram of the square and the triangle is shown. Consider the triangles $P Q T$ and $R Q T$. They share side $Q T$; also $P Q=R Q$ because they are sides of a square; and $P T=R T$ because they are sides of the equilateral triangle, so by SSS the triangles $P Q T$ and $R Q T$ are congruent. Therefore $\angle P Q T=\angle R Q T$. Also $\angle P Q T+\angle R Q T+90^{\circ}=360^{\circ}$ so $\angle R Q T=\frac{1}{2}\left(360^{\circ}-90^{\circ}\right)=135^{\circ}$.