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From the image, it appears that you're working on a problem where two angles form a linear pair. One of the angles is described as being 15 degrees less than \(\frac{2}{3}\) of the other angle, and you are asked to find both angles.

### Step-by-Step Solution:

1. **Identify the relationship:**
   - Let the larger angle be \( x \).
   - The smaller angle is given as \( \frac{2}{3}x - 15 \).

2. **Equation setup:**
   Since the two angles form a linear pair, their sum must be 180 degrees (because the sum of angles in a linear pair is always 180 degrees):
   \[
   x + \left( \frac{2}{3}x - 15 \right) = 180
   \]

3. **Solve the equation:**
   Start by simplifying the equation:
   \[
   x + \frac{2}{3}x - 15 = 180
   \]
   Combine the terms involving \(x\):
   \[
   \frac{3}{3}x + \frac{2}{3}x = \frac{5}{3}x
   \]
   So, the equation becomes:
   \[
   \frac{5}{3}x - 15 = 180
   \]
   Add 15 to both sides:
   \[
   \frac{5}{3}x = 195
   \]
   Multiply both sides by 3 to eliminate the fraction:
   \[
   5x = 585
   \]
   Divide by 5:
   \[
   x = 117
   \]
   Thus, the larger angle is \(117^\circ\).

4. **Find the smaller angle:**
   The smaller angle is:
   \[
   \frac{2}{3}x - 15 = \frac{2}{3}(117) - 15 = 78 - 15 = 63^\circ
   \]

### Final Answer:
- The measure of the larger angle is **117 degrees**.
- The measure of the smaller angle is **63 degrees**.

Let me know if you'd like more details on any of these steps!

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Here are 5 questions to test your understanding:
1. How do you identify a linear pair of angles?
2. Why is the sum of angles in a linear pair always 180 degrees?
3. Can you explain how we combined the fractions when solving for \(x\)?
4. What would happen if the relationship between the angles was different (e.g., the smaller angle was more than \( \frac{2}{3} \) of the larger angle)?
5. Can you apply this method to find angles that form a complementary pair (sum is 90 degrees)?

**Tip**: Always check if the problem involves complementary (sum = 90°) or supplementary (sum = 180°) angles to set up the correct equation.

Two angles form a linear pair. The measure of one angle is 15 degrees less than two-thirds the measure of the other angle. Find the measure of each angle.

Solve a problem involving two angles forming a linear pair, where one angle is 15 degrees less than two-thirds of the other. This problem applies algebraic methods to calculate the angles, suitable for students in Grades 7-9.

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