https://file.aiquickdraw.com/mathbot/file/17309536802549d2bnvkx.jpg

To solve for \( x \) and \( y \) in this triangle, let's analyze each angle step by step.

1. **Identify the known angles**:
   - There is a right angle, meaning one angle is \( 90^\circ \).
   - The angle labeled \( 25^\circ \) at the top.
   - The angle labeled \( 20^\circ \) at the bottom right.

2. **Calculate angle \( x \)**:
   - Since \( x \) and \( 25^\circ \) are complementary with the right angle below, we have:
     \[
     x = 90^\circ - 25^\circ = 65^\circ
     \]

3. **Calculate angle \( y \)**:
   - In the large triangle, the sum of the angles must be \( 180^\circ \).
   - We already know two angles: \( 90^\circ \) (the right angle) and \( 20^\circ \).
   - Thus,
     \[
     y = 180^\circ - 90^\circ - 20^\circ = 70^\circ
     \]

Therefore:
- \( x = 65^\circ \)
- \( y = 70^\circ \)

Would you like further explanation or have any other questions?

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### Related Questions:
1. How would the solution change if the given angles were different?
2. Can we apply these angle-sum rules to any triangle configuration?
3. How does understanding complementary angles help in such problems?
4. What are other common relationships between angles in right triangles?
5. How can trigonometric functions be used to find unknown sides in this triangle?

### Tip:
Always double-check the sum of angles in a triangle to ensure they add up to \( 180^\circ \), especially when working with right triangles.

Find the values of x and y in the given triangle.

Solve for the unknown angles x and y in a triangle where one angle is 25° and another is 20°, and a right angle is present. Learn how to apply the triangle sum theorem and complementary angle relationships in geometry.

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