https://file.aiquickdraw.com/mathbot/file/1727118805918d0k6dgtw.jpg

The diagram you uploaded shows several angles formed by intersecting lines. We are tasked with finding the missing angles \(x\) and \(y\).

### Step-by-step solution:

1. **Identify known angles and relationships**:
   - The diagram shows a 90° angle in the lower-right quadrant, which splits the vertical and horizontal lines.
   - The angle labeled 38° shares a straight line with angle \(x\), meaning these two angles are supplementary. So, \(x + 38^\circ = 180^\circ\).

2. **Find angle \(x\)**:
   Using the supplementary angle relationship:
   \[
   x = 180^\circ - 38^\circ = 142^\circ
   \]

3. **Find angle \(y\)**:
   The sum of the angles around the point where \(y\) and the 90° angle meet must equal 180° because they form a straight line.
   \[
   y + 90^\circ = 180^\circ
   \]
   Solving for \(y\):
   \[
   y = 180^\circ - 90^\circ = 90^\circ
   \]

### Final Answer:
- \(x = 142^\circ\)
- \(y = 90^\circ\)

Would you like further clarification on these steps or more detailed explanations?

Here are 5 related questions for practice:
1. If an angle is complementary to \(y\), what is its measure?
2. What would the measure of \(x\) be if the angle adjacent to it was 40° instead of 38°?
3. What are supplementary angles, and why are \(x\) and 38° supplementary?
4. If the angle \(x\) was bisected, what would each smaller angle measure?
5. Can a right angle ever be supplementary? Explain why or why not.

**Tip**: Remember that supplementary angles always add up to 180°, while complementary angles sum to 90°.

Find the measure of the missing angles (x and y) based on a diagram with an angle of 38 degrees and a right angle.

Learn how to find the missing angles in a geometric diagram involving supplementary angles and a right angle. This problem covers key geometric concepts and formulas. Suitable for students in Grades 6-8.

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