https://file.aiquickdraw.com/mathbot/file/17274527231533fauu9zi.jpg

Let's solve the problems one by one from the image you've uploaded.

### Problem 1:
You need to find the third angle in the triangle, knowing that the sum of angles in any triangle is 180 degrees.

Given angles:
- \(80^\circ\)
- \(39^\circ\)

To find the third angle, \(?\), we use the formula:
\[ \text{Angle } ? = 180^\circ - 80^\circ - 39^\circ \]

### Problem 2:
The diagram shows an exterior angle, \(?\), and two opposite interior angles (82° and 42°).

The measure of the exterior angle of a triangle is equal to the sum of the two opposite interior angles, so:
\[ \text{Angle } ? = 82^\circ + 42^\circ \]

Let me calculate these for you.### Solutions:

**Problem 1:** The third angle in the triangle is \(61^\circ\).

**Problem 2:** The exterior angle, indicated by \(?\), measures \(124^\circ\).

Would you like to go through any of these in more detail or need help with other problems from the image?

**Further Questions:**
1. How would you find an exterior angle if only two interior angles are given?
2. What happens to the angles in a triangle if it is right, acute, or obtuse?
3. Can a triangle have more than one right angle? Why or why not?
4. How do the properties of angles apply to real-world constructions?
5. What is the significance of knowing how to calculate exterior angles in geometric design?

**Tip:** When solving for unknown angles in triangles, always ensure that the sum of all interior angles equals 180 degrees as a quick check on your calculations.

Find the measure of each angle indicated and solve for x in the given triangle problems.

This practice problem focuses on finding unknown angles in triangles using the Triangle Sum Theorem and Exterior Angle Theorem. Solutions include calculating interior and exterior angles in various triangle setups, suitable for 8th-grade students.

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