https://file.aiquickdraw.com/mathbot/file/1726548264105e0neo5b0.jpg

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.

In the diagram, chords QW = RW. Given that ∠QWR = 40° and ∠WRT = 35°, determine the value of ∠QSR, ∠WQT, ∠WRQ, and ∠QRT.

Learn how to solve a circle geometry problem involving chords QW and RW with given angles QWR = 40° and WRT = 35°. Explore key geometry concepts such as the angle at the center theorem, isosceles triangles, and angle properties of circles.

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