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