Let's analyze the given problem:

1. Given Information:

   • $QW = RW$ (chords $QW$ and $RW$ are equal)
   • $\angle QWR = 40^\circ$
   • $\angle WRT = 35^\circ$
   • We need to find the values of the following angles: a) $\angle QSR$
     b) $\angle WQT$
     c) $\angle WRQ$
     d) $\angle QRT$

2. Interpretation and Solution:

   • Since $QW = RW$, triangle $QWR$ is isosceles with $\angle WQR = \angle WRQ$.
   • Given $\angle QWR = 40^\circ$, the sum of the angles in triangle $QWR$ is $180^\circ$.
   • Let $\angle WQR = \angle WRQ = x$. So, $x + x + 40^\circ = 180^\circ$.
   • $2x + 40^\circ = 180^\circ$
   • $2x = 140^\circ$
   • $x = 70^\circ$
   • Therefore, $\angle WQR = \angle WRQ = 70^\circ$.

   Now, let's determine each of the angles specified in the choices:

   a) $\angle QSR$:

   • From the given image and using the angle at the center theorem: $\angle QSR = \frac{1}{2} \times \angle QWR$
   • Since $\angle QWR = 40^\circ$, $\angle QSR = 20^\circ$.

   b) $\angle WQT$:

   • This angle is part of $\triangle QWT$ where $\angle QWR = 40^\circ$ and $\angle WRT = 35^\circ$. Since $QW = RW$, $\triangle QWT$ is isosceles.
   • Therefore, $\angle WQT = \angle WRT = 35^\circ$.

   c) $\angle WRQ$:

   • We already determined this as $70^\circ$.

   d) $\angle QRT$:

   • The external angle $\angle QRT = \angle QWR + \angle WRT = 40^\circ + 35^\circ = 75^\circ$.

So the values are:

• $\angle QSR = 20^\circ$
• $\angle WQT = 35^\circ$
• $\angle WRQ = 70^\circ$
• $\angle QRT = 75^\circ$

Only $\angle WQT = 35^\circ$ corresponds with one of the options provided in the question.

Would you like further clarification or a detailed explanation of any part?

Here are some related questions for further practice:

1. What are the properties of an isosceles triangle in a circle?
2. How do the angles subtended by the same arc in a circle relate to each other?
3. What is the relationship between the angle at the center and the angle at the circumference in a circle?
4. How do you find the external angles of a triangle?
5. How does the angle bisector theorem apply to circles?

Tip: Always look for equal chords and isosceles triangles when dealing with angles in circles; they often help in simplifying angle calculations.