https://file.aiquickdraw.com/mathbot/file/1729016994884w0eplz5f.jpg

The diagram shows two missing angles, \(x\) and \(y\), along with a given angle of \(64^\circ\). Let's break this down to find the missing angles.

### Step-by-step solution:

1. **Identify angle \(x\):**
   - The angle \(x\) and the given angle of \(64^\circ\) are supplementary, meaning they form a straight line. Therefore, the sum of these two angles is \(180^\circ\).
   \[
   x + 64^\circ = 180^\circ
   \]
   Solving for \(x\):
   \[
   x = 180^\circ - 64^\circ = 116^\circ
   \]

2. **Identify angle \(y\):**
   - The angle \(y\) is complementary to the given right angle (since it forms part of the right-angled corner in the diagram). The sum of complementary angles is \(90^\circ\).
   \[
   y + 64^\circ = 90^\circ
   \]
   Solving for \(y\):
   \[
   y = 90^\circ - 64^\circ = 26^\circ
   \]

### Final answers:
- \(x = 116^\circ\)
- \(y = 26^\circ\)

Let me know if you want further clarifications or details!

Here are some related questions to expand your understanding:
1. What are supplementary angles?
2. How do complementary angles relate to right angles?
3. Can the value of \(x\) change if the given angle was not 64°?
4. How do we identify which angles are supplementary or complementary in a given diagram?
5. What are vertical angles and how are they calculated?

**Tip:** Always check if angles form a straight line (supplementary) or a right angle (complementary) to simplify your calculations.

Find the measure of the missing angles: Given a diagram with angles x and y, and an angle of 64°.

Solve a geometry problem to find the missing angles x and y, given one angle of 64°. Learn how to use supplementary and complementary angle theorems. Suitable for Grades 6-8.

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