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The diagram provided is of a triangle with various angles marked. Let me help you by calculating the unknown angles based on the given information.

### Given Data:
1. ∠Q = 60°
2. ∠P = 55°
3. ∠R = 40°
4. ∠S is split into three angles: a, b, and c.

We are tasked with finding the values of angles \(a\), \(b\), and \(c\).

### Solution Approach:
1. **Step 1: Triangle QPR**
   - In any triangle, the sum of interior angles is always 180°.
   - In triangle \( \triangle QPR \), we have:
     \[
     \text{Sum of angles} = 180°
     \]
     \[
     ∠Q + ∠P + ∠R = 180°
     \]
     Substituting the known angles:
     \[
     60° + 55° + 40° = 155°
     \]
     So, the remaining angle at vertex \(S\) (which splits into \(a\), \(b\), and \(c\)) is:
     \[
     180° - 155° = 25°
     \]

2. **Step 2: Relation between a, b, and c**
   Since angle \(a\), \(b\), and \(c\) form supplementary angles (angles on a straight line sum up to 180°), we can conclude:
   \[
   a + b + c = 180°
   \]
   
3. **Step 3: Angle c**
   Notice that \( ∠c = 55° \), as it's opposite the known angle at vertex P in triangle QPR.

4. **Step 4: Calculate angle a and b**
   - Now, since \( a + b = 25° \) (calculated in step 1), and angle \(b = 40°\), we can now find angle \(a\).
   \[
   a = 25° - b
   \]
   \[
   a = 25° - 40° = -15°
   \]
   
   Given this result doesn't seem geometrically correct, it implies a miscalculation or something

Find the values of angles a, b, and c in the given triangle.

In this geometry problem, you will learn how to find unknown angles a, b, and c in a triangle using the triangle angle sum theorem and supplementary angles on a straight line. This problem involves calculating angles for a triangle where the angles at one vertex are split into three parts.

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