If 
GI
 and 
JL
 are parallel lines and mIHK= 41°, what is mGHK?


To solve this, we need to apply the properties of parallel lines and angles formed by a transversal. Here’s the given information:

- \( GI \parallel JL \) (meaning lines \( GI \) and \( JL \) are parallel).
- \( \angle IHK = 41^\circ \) (this is the given angle measure).

We are asked to find \( m \angle GHK \).

### Steps:
1. Since \( GI \parallel JL \), and \( \overline{HK} \) serves as a transversal, the angle \( \angle IHK \) forms a pair with \( \angle GHK \).
   
2. \( \angle IHK \) and \( \angle GHK \) are **alternate interior angles** because they are on opposite sides of the transversal \( \overline{HK} \), and alternate interior angles are congruent when the lines are parallel.

3. Therefore, \( m \angle GHK = m \angle IHK = 41^\circ \).

Thus, the measure of \( \angle GHK \) is **41°**.

Would you like more details or have any questions?

Here are 5 related questions:
1. What are corresponding angles and when do they occur?
2. How do alternate interior angles behave when lines are not parallel?
3. How would you solve for the unknown angle if the lines weren’t parallel?
4. Can alternate exterior angles be used to solve problems involving parallel lines?
5. How does the transversal affect the types of angles formed?

**Tip:** Always look for parallel lines when dealing with angles, as they can simplify finding unknown angle measures.

If GI and JL are parallel lines and mIHK= 41°, what is mGHK?

Discover how to find the measure of angle GHK given parallel lines GI and JL with a transversal. Using the Alternate Interior Angles Theorem, we solve for the unknown angle when mIHK = 41°. Suitable for students in Grades 8-10.

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