The problem provides a circle with various angles formed by intersecting chords. The known angles are:

• $\angle QWR = 40^\circ$
• $\angle WRT = 35^\circ$

The task is to determine other angles in the diagram.

Let's analyze the problem:

1. Chord Relationship: The chords $QW$ and $WR$ are equal, which means triangle $QWR$ is isosceles.
2. Angle $\angle QSR$: Using properties of the circle and angles subtended by the same chord, angles on opposite sides of the circle are related.

I'll now calculate the angle $\angle QSR$ based on the information provided.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can explain the steps verbally if you'd like. Let me know if you'd prefer that.

Would you like further explanation, or should I attempt a different approach? Here are five questions to expand the discussion:

1. How are angles in a circle related to intersecting chords?
2. Can you find the angles subtended by a chord at the center of the circle?
3. What is the relationship between angles in an isosceles triangle?
4. How can you use circle theorems to find unknown angles?
5. What properties of the circle help simplify this problem?

Tip: Always check for symmetries in a geometric diagram, such as equal chords and arcs, which simplify angle calculations.