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The image shows a problem asking to find the measures of two angles with the following given information:

- One angle is represented as \(3x + 2\) degrees.
- The other angle is represented as \(5x + 8\) degrees.
- The two angles are likely part of a straight line, which means they are supplementary. Supplementary angles sum up to \(180^\circ\).

### Let's solve for \(x\) and find the measure of each angle:

1. Since the angles are supplementary, their sum should equal \(180^\circ\):
   \[
   (3x + 2) + (5x + 8) = 180
   \]

2. Simplify the equation:
   \[
   3x + 5x + 2 + 8 = 180
   \]
   \[
   8x + 10 = 180
   \]

3. Subtract 10 from both sides:
   \[
   8x = 170
   \]

4. Solve for \(x\):
   \[
   x = \frac{170}{8} = 21.25
   \]

Now that we have the value of \(x = 21.25\), we can find the measures of each angle:

- \(3x + 2 = 3(21.25) + 2 = 63.75 + 2 = 65.75^\circ\)
- \(5x + 8 = 5(21.25) + 8 = 106.25 + 8 = 114.25^\circ\)

Thus, the two angles are approximately:
- \(65.75^\circ\)
- \(114.25^\circ\)

These two angles sum to \(180^\circ\), confirming that the solution is correct.

Would you like more details or clarifications on this solution?

### Related questions:
1. What are complementary angles, and how are they different from supplementary angles?
2. How do you find the measure of angles formed by parallel lines and a transversal?
3. Can angles larger than \(180^\circ\) exist in Euclidean geometry?
4. How would you solve for \(x\) if the angles formed were complementary instead of supplementary?
5. What is the importance of alternate interior angles in geometry?

### Tip:
When solving for angles in geometry, always check whether they form complementary, supplementary, or vertical pairs to use the appropriate relationships.

Find the measure of each angle. The angles are given by the expressions 3x + 2 and 5x + 8. The sum of these angles is 180 degrees, indicating they are supplementary angles.

Find the measures of two angles where one angle is represented as 3x + 2 and the other as 5x + 8. Learn to use the supplementary angles theorem to solve linear equations in geometry. This problem is ideal for students in Grades 7-9.

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