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The problem in the image asks to find the measures of angles 1 through 5 in a triangle figure. Here's a breakdown of how we can approach it based on the given information:

- The triangle is labeled with angles 1, 2, 3, 4, and 5.
- One angle is marked as **68°** and another as **52°**, which likely refers to the internal angles of the triangle.
- There is also a right angle (marked by a square in the figure).

### Step-by-Step Solution:

1. **Angle 3 (Right Angle)**: 
   The symbol shows that Angle 3 is a right angle. Therefore, angle 3 = **90°**.

2. **Angle 1 (In a Triangle)**:
   The sum of the interior angles in any triangle is always 180°. We already know two angles:
   - Angle 3 = 90° (from the right angle)
   - Angle 2 = 52°
   
   Using the sum of interior angles in the triangle:
   \[
   \text{Angle 1} + \text{Angle 2} + \text{Angle 3} = 180°
   \]
   Substituting the known values:
   \[
   \text{Angle 1} + 52° + 90° = 180°
   \]
   Simplifying:
   \[
   \text{Angle 1} = 180° - 142° = 38°
   \]

3. **Angle 4 and Angle 5 (Supplementary and Vertical Angles)**:
   - Angle 4 and the 68° angle form a linear pair (they are on a straight line). The sum of angles on a straight line is 180°, so:
   \[
   \text{Angle 4} + 68° = 180°
   \]
   Therefore:
   \[
   \text{Angle 4} = 180° - 68° = 112°
   \]
   - Since angles 5 and 4 are vertical angles (formed by intersecting lines), they are equal:
   \[
   \text{Angle 5} = 112°
   \]

### Final Answer:
- **Angle 1 = 38°**
- **Angle 2 = 52°**
- **Angle 3 = 90°**
- **Angle 4 = 112°**
- **Angle 5 = 112°**

Would you like any more details or clarification? 

Here are 5 related questions for further practice:
1. How do you find the third angle in a triangle if two angles are known?
2. What are vertical angles, and how are they related to intersecting lines?
3. How do you determine supplementary angles on a straight line?
4. What are the properties of right triangles?
5. How can you calculate exterior angles in a triangle?

**Tip:** Remember, vertical angles are always equal, and supplementary angles always add up to 180°.

Find the measures of angles 1 through 5 in the figure shown.

Learn how to find the measures of angles in a triangle using the sum of interior angles, vertical angles, and supplementary angles. This problem involves understanding right triangles, linear pairs, and basic geometry, suitable for students in Grades 7-9.

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