11. In the diagram, lines $Q T$ and $R S$ are parallel and $P Q$ and $Q T$ are equal. Angle $S T Q$ is $154^{\circ}$. What is the size of angle $S R Q$ ?
A $120^{\circ}$
B $122^{\circ}$
C $124^{\circ}$
D $126^{\circ}$
E $128^{\circ}$
Solution
E

Since $\angle S T Q=154^{\circ}$ and angles on a straight line add to $180^{\circ}, \angle P T Q=26^{\circ}$. Hence, since $P Q$ and $Q T$ are equal, triangle $P T Q$ is isosceles and so $\angle T P Q=26^{\circ}$. Therefore, since angles in a triangle add to $180^{\circ}, \angle T Q P=128^{\circ}$. Finally, since $Q T$ and $R S$ are parallel and corresponding angles on parallel lines are equal, $\angle S R Q=128^{\circ}$.