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.