https://file.aiquickdraw.com/mathbot/file/1727889730781hy410r3z.jpg

The problem is asking to find the measure of angle \( \angle GHJ \), given that lines \( \overleftrightarrow{DF} \) and \( \overleftrightarrow{GI} \) are parallel, and \( m\angle FEC = 58^\circ \).

### Solution:
1. Since \( \overleftrightarrow{DF} \) and \( \overleftrightarrow{GI} \) are parallel, the transversal \( \overleftrightarrow{HE} \) forms alternate interior angles with these lines.
2. Angle \( \angle FEC \) and angle \( \angle GHJ \) are alternate interior angles because \( \overleftrightarrow{HE} \) is the transversal intersecting the two parallel lines.
3. According to the Alternate Interior Angles Theorem, alternate interior angles are congruent. This means \( \angle GHJ = \angle FEC \).

Therefore, \( m\angle GHJ = 58^\circ \).

Let me know if you'd like further details or explanations!

### Related Questions:
1. What is the Alternate Interior Angles Theorem?
2. How do you identify transversal lines in a geometry diagram?
3. What other angle relationships are formed by parallel lines and a transversal?
4. Can you explain how corresponding angles differ from alternate interior angles?
5. How does the Same-Side Interior Angles Theorem apply to this diagram?

**Tip:** When working with parallel lines, identifying transversals and corresponding angle pairs can help solve many problems quickly.

If DF and GI are parallel lines and m∠FEC = 58°, what is m∠GHJ?

Solve for m∠GHJ in a diagram with parallel lines DF and GI, using the given m∠FEC = 58°. Learn how to apply the Alternate Interior Angles Theorem to find the unknown angle.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation