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Let's analyze the problem step-by-step.

### Given:
- Angle labeled \(134^\circ\) (top right corner).
- A vertical and horizontal intersecting set of lines with labeled missing angles \(d\), \(e\), and \(f\).
- \(d\) is part of a right angle (90° with the horizontal line).
  
We need to determine the values of \(d\), \(e\), and \(f\).

---

### 1. Solve for \(e\):
- \(e\) and the given angle \(134^\circ\) are **supplementary** (they lie on a straight line), meaning:
  \[
e + 134^\circ = 180^\circ
  \]
  Solving for \(e\):
  \[
e = 180^\circ - 134^\circ = 46^\circ
  \]

---

### 2. Solve for \(f\):
- \(e\) and \(f\) are **vertically opposite angles**, so:
  \[
f = e = 46^\circ
  \]

---

### 3. Solve for \(d\):
- \(d\) is part of a **right angle** with the vertical line, meaning:
  \[
d + f = 90^\circ
  \]
  Substituting \(f = 46^\circ\):
  \[
d = 90^\circ - 46^\circ = 44^\circ
  \]

---

### Final Answers:
\[
d = 44^\circ, \quad e = 46^\circ, \quad f = 46^\circ
\]

---

Do you want me to explain any part in more detail, or clarify further?

Here are 5 follow-up questions to expand your understanding:
1. What are vertically opposite angles, and how are they formed?
2. How do you recognize when two angles are supplementary?
3. How does the concept of complementary angles apply to this problem?
4. Can a triangle have angles that sum to more than 180 degrees?
5. How would you solve if the given angle was a reflex angle instead?

**Tip:** Always check for angle pairs—like complementary, supplementary, or vertically opposite—to solve problems efficiently.

Find the measure of the missing angles: d, e, and f in a geometry problem where the given angle is 134°, and the lines form vertical, horizontal, and intersecting angles.

This problem focuses on solving for missing angles d, e, and f using the given angle of 134°. It involves understanding supplementary angles, vertically opposite angles, and complementary angles. Suitable for students in Grades 6-8.

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