To solve for $x^\circ$ and $y^\circ$ in the given diagram, we can use the properties of triangles.

Step 1: Find $x^\circ$

The top triangle is a triangle with two known angles: 25° and $x^\circ$. The sum of angles in any triangle must be 180°. $x^\circ + 25^\circ + 90^\circ = 180^\circ$ Solving for $x^\circ$: $x^\circ = 180^\circ - 25^\circ - 90^\circ = 65^\circ$

Step 2: Find $y^\circ$

Now, consider the right triangle at the bottom. The sum of the angles in this triangle is also 180°. Since one of the angles is 90° and another is 20°, we can find $y^\circ$ as follows: $y^\circ + 90^\circ + 20^\circ = 180^\circ$ Solving for $y^\circ$: $y^\circ = 180^\circ - 90^\circ - 20^\circ = 70^\circ$

Final Answers:

$x = 65^\circ, \quad y = 70^\circ$

Would you like more details or have any other questions?

Here are five related questions to deepen your understanding:

1. How do the angles in a triangle always sum up to 180°?
2. What would happen if one of the angles was 30° instead of 25°?
3. Can you identify the types of triangles based on their angles?
4. How does the right angle (90°) affect the calculations of other angles?
5. What are the exterior angles of a triangle, and how do they relate to the interior ones?

Tip: Always remember that the sum of angles in any triangle is always 180°.