In the given image, we have a triangle with several labeled angles. Let's analyze the problem and solve for the angles denoted by the lowercase letters $a$, $b$, and $c$.

Step-by-Step Analysis:

1. The triangle shows the following given angles:

   • One angle marked as $45^\circ$.
   • One angle marked as $20^\circ$.
   • One angle marked as $60^\circ$.

2. The angle at the bottom right is labeled $c$, the angle near the middle (on the larger triangle) is labeled $b$, and the angle at the bottom left is labeled $a$.

Strategy to solve:

• We will use the fact that the sum of angles in a triangle always adds up to $180^\circ$.

For the larger triangle:

• The three angles in the larger triangle include the two given angles $60^\circ$ and $b$, plus the angle that is the sum of $45^\circ + 20^\circ$ (the upper left corner angle).

  • The upper left corner is composed of $45^\circ$ and $20^\circ$, so the total for that corner is $65^\circ$.

  Now, we can find $b$: $b = 180^\circ - (60^\circ + 65^\circ) = 180^\circ - 125^\circ = 55^\circ$

For the smaller triangle on the right:

• The angles in the smaller triangle include the angle labeled $a$, the given $20^\circ$, and the angle $b = 55^\circ$.
  • Since the sum of angles in a triangle is $180^\circ$: $a = 180^\circ - (55^\circ + 20^\circ) = 180^\circ - 75^\circ = 105^\circ$

Conclusion:

• $b = 55^\circ$
• $a = 105^\circ$
• The angle $c$ is already given as $60^\circ$.

Let me know if you'd like further details or clarifications!

Here are some follow-up questions for practice:

1. What is the sum of interior angles in a triangle?
2. Can you calculate the third angle of a triangle if two angles are given as $40^\circ$ and $70^\circ$?
3. How do we use the exterior angle theorem in a triangle?
4. If an exterior angle of a triangle is $120^\circ$, what can we say about the sum of the opposite interior angles?
5. In an isosceles triangle with two equal angles of $70^\circ$, what is the value of the third angle?

Tip: Always double-check the given angles in geometric figures to ensure consistency in your calculations!