To solve for the missing angles $x$ and $y$, let's analyze the diagram where one of the angles is given as 24° and another angle is a right angle (90°).

Step 1: Understand the Relationships Between Angles

• Angle $x$: Angle $x$ and the 24° angle are complementary because together with the right angle (90°), they form a straight line (which totals 180°). Therefore: $x + 24^\circ + 90^\circ = 180^\circ$ Solving for $x$: $x = 180^\circ - 90^\circ - 24^\circ = 66^\circ$

• Angle $y$: Angle $y$ and $x$ are vertically opposite angles, so: $y = x = 66^\circ$

Step 2: Conclusion

• $x = 66^\circ$
• $y = 66^\circ$

Would you like more details or have any further questions?

Related Questions:

1. What are complementary angles, and how are they used in geometry?
2. How do you determine if two angles are vertically opposite?
3. What is the sum of angles around a point, and how is this useful?
4. Can a right angle be vertically opposite to another right angle?
5. How can you use the properties of angles to solve real-world problems?

Tip:

Remember, angles on a straight line always sum to 180°, and complementary angles sum to 90°. This can help you easily solve various angle-related problems!