If 
DF
 and 
GI
 are parallel lines and mDEC = 134°, what is mGHE?


Given that lines \( DF \) and \( GI \) are parallel, and you know the measure of angle \( \text{m}\angle DEC = 134^\circ \), the goal is to find the measure of angle \( \text{m}\angle GHE \).

Since \( DF \parallel GI \), angles \( \angle DEC \) and \( \angle GHE \) are corresponding angles (assuming \( \angle DEC \) and \( \angle GHE \) are in corresponding positions relative to the parallel lines and a transversal).

### Properties Used:
1. **Corresponding Angles Postulate**: When two parallel lines are cut by a transversal, the pairs of corresponding angles are congruent.

### Solution:
\[
\text{m}\angle GHE = \text{m}\angle DEC = 134^\circ
\]

So, the measure of angle \( \text{m}\angle GHE \) is \( 134^\circ \).

Would you like more details, or do you have any questions? Here are five related questions for further practice:

1. If \( \text{m}\angle GHE \) is \( 134^\circ \), what would be the measure of \( \text{m}\angle HEC \) assuming it forms a linear pair with \( \text{m}\angle GHE \)?
2. What is the measure of \( \text{m}\angle EDC \) if \( DF \parallel GI \) and \( \text{m}\angle GHE = 134^\circ \)?
3. If \( \text{m}\angle DEC = 134^\circ \), what is the measure of \( \text{m}\angle EDF \) assuming it is on the opposite side of the transversal from \( \angle DEC \)?
4. How would the situation change if the lines \( DF \) and \( GI \) were not parallel?
5. Can you find the measure of any alternate interior angles given \( DF \parallel GI \) and \( \text{m}\angle DEC = 134^\circ \)?

### Tip:
Always remember that corresponding angles formed by a transversal with two parallel lines are congruent.

If DF and GI are parallel lines and mDEC = 134°, what is mGHE?

Explore how to determine the measure of angle GHE when given that lines DF and GI are parallel, and mDEC = 134°. This problem utilizes the corresponding angles postulate and is suitable for students in Grades 8-10.

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