https://file.aiquickdraw.com/mathbot/file/1727287455168b0qmbwfx.jpg

In this diagram, we are asked to analyze the relationship between ∠4 and ∠5, given that BA ∥ DC.

### Step 1: Identify the type of angle pair.
∠4 and ∠5 are positioned such that one is on the interior left side of the transversal \( \overline{AC} \), while the other is on the interior right side of the transversal \( \overline{AC} \). These angles lie on opposite sides of the transversal and between the parallel lines \( \overline{BA} \parallel \overline{DC} \). 

This setup defines **alternate interior angles**.

### Step 2: Determine whether the angles are congruent or supplementary.
By the **Alternate Interior Angles Theorem**, alternate interior angles are **congruent** when two parallel lines are cut by a transversal.

Thus, **∠4 and ∠5 are congruent**.

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Here are 5 related questions to deepen your understanding:

1. What theorem guarantees that alternate interior angles are congruent when two lines are parallel?
2. How do you identify supplementary angles in such geometric configurations?
3. Can ∠1 and ∠8 be considered congruent in this diagram? Why or why not?
4. What is the sum of the measures of two supplementary angles?
5. How would the result change if \( \overline{BA} \) and \( \overline{DC} \) were not parallel?

**Tip:** Always remember that congruent angles have equal measures, whereas supplementary angles sum up to 180°.

Given that BA || DC, select which type of angle this pair is and then tell whether it is congruent or supplementary for ∠4 and ∠5.

Learn how to determine whether ∠4 and ∠5, formed by parallel lines BA || DC and transversal AC, are congruent or supplementary using the Alternate Interior Angles Theorem. This geometry problem is suitable for students in Grades 8-10.

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