https://file.aiquickdraw.com/mathbot/file/17259275376681ahmlmd5.jpg

To solve for the missing angles \(d\), \(e\), and \(f\), we need to analyze the geometric relationships in the diagram.

### Step-by-Step Solution:

1. **Angle \(d\):** 
   - Notice that angle \(d\) is adjacent to a right angle. Therefore, angle \(d = 90^\circ\).

2. **Angle \(e\):** 
   - Angles \(e\) and the \(151^\circ\) angle form a linear pair (they are on a straight line).
   - Therefore, \(e + 151^\circ = 180^\circ\).
   - Solving for \(e\):  
   \[
   e = 180^\circ - 151^\circ = 29^\circ.
   \]

3. **Angle \(f\):** 
   - Angles \(e\) and \(f\) are vertically opposite angles, so they are equal.
   - Therefore, \(f = e = 29^\circ\).

### Final Answer:
- \(d = 90^\circ\)
- \(e = 29^\circ\)
- \(f = 29^\circ\)

Would you like more details or have any other questions?

### Related Questions:
1. How do you find the measure of a supplementary angle?
2. What are vertically opposite angles and why are they equal?
3. Can you explain why the sum of angles on a straight line is always \(180^\circ\)?
4. How do you determine the type of angles formed by intersecting lines?
5. What is the definition of a linear pair of angles?

**Tip:** Remember, angles that are on a straight line always add up to \(180^\circ\).

Find the measure of the missing angles d, e, and f.

Solve for the missing angles d, e, and f in a geometry problem involving a straight line and vertical angles. Learn about linear pairs and why vertical angles are equal. Suitable for students in Grades 6-8.

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