https://file.aiquickdraw.com/mathbot/file/17264586684438nn6llf1.jpg

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!

Find the magnitude of each angle denoted by a lowercase letter in this figure.

Learn how to solve for the unknown angles labeled 'a', 'b', and 'c' in a triangle using the triangle angle sum theorem. Given angles of 45°, 20°, and 60°, find the remaining angles with step-by-step calculations. Suitable for students in Grades 7-9.

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