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We are given a diagram where \( \overleftrightarrow{DF} \) and \( \overleftrightarrow{GI} \) are parallel lines, and the measure of \( \angle GHJ = 132^\circ \). We are asked to find the measure of \( \angle GHE \).

### Step-by-step solution:

1. **Identify the angle relationships:**
   - Since \( \overleftrightarrow{DF} \parallel \overleftrightarrow{GI} \) and \( \overleftrightarrow{HJ} \) is a transversal, the angles formed around point \( H \) are related by the properties of parallel lines.
   - \( \angle GHJ \) and \( \angle GHE \) are **alternate interior angles**, meaning they are congruent.

2. **Use the given information:**
   - Since \( \angle GHJ = 132^\circ \) and \( \angle GHE \) is an alternate interior angle, we conclude:
   \[
   m\angle GHE = m\angle GHJ = 132^\circ.
   \]

Thus, the measure of \( \angle GHE \) is \( 132^\circ \).

Would you like further clarification or details?

### Related questions:
1. What are corresponding angles, and how do they relate to parallel lines?
2. How do you find the measure of an exterior angle when given an interior angle?
3. What are the properties of transversals when intersecting two parallel lines?
4. Can alternate exterior angles also be congruent? Why or why not?
5. How can we use the concept of supplementary angles in parallel line problems?

### Tip:
Always look for relationships like alternate interior, corresponding, or supplementary angles when working with parallel lines and transversals. These are key to solving most geometry problems involving parallel lines.

If DF and GI are parallel lines and m∠GHJ = 132°, what is m∠GHE?

Learn how to find the measure of angle GHE when given that DF and GI are parallel lines and m∠GHJ = 132°. This problem involves the Alternate Interior Angles Theorem, which applies to parallel lines and a transversal.

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