To determine whether the statements ∠6 = 28° and ∠5 = 28° are true or false, we can use the properties of parallel lines and transversals.
Since lines A and B are parallel, and a transversal crosses them, we can identify several relationships between the angles.
- Identify the angle properties:
- When a transversal crosses parallel lines, corresponding angles are equal.
- Alternate interior angles are equal.
- Consecutive interior angles are supplementary (add up to 180°).
Given that one angle is labeled 28°, let's define the angles based on their relationships with the 28° angle:
- If we assume the angle labeled 28° is ∠1, then:
- For ∠6: If ∠6 is a corresponding angle to ∠1 (for example, on line B in the same relative position), then ∠6 = 28° would be true.
- For ∠5: If ∠5 is an alternate interior angle to ∠1, then ∠5 = 28° would also be true.
- Filling the table:
- Statement: ∠6 = 28°
- If ∠6 is appropriately positioned as a corresponding angle, this statement is True.
- Statement: ∠5 = 28°
- If ∠5 is an alternate interior angle to ∠1, this statement is also True.
- Statement: ∠6 = 28°
Conclusion:
- ∠6 = 28°: True
- ∠5 = 28°: True
Without the actual figure, I assumed the common relationships for angles when dealing with parallel lines and a transversal. Please adjust based on the specific arrangement shown in your figure.
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