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°.