Question
In the figure, one angle is labeled 28° (number 3), and lines A and B are parallel. Complete the table. For each statement, select True or False. Show your work. True False∠5 = 28°∠6 = 28°
Answers
GPT-4o mini
To determine the truth value of each statement regarding angles formed by parallel lines and a transversal, we need to identify the relationships between the angles.
Given:
- Lines A and B are parallel.
- One angle (which we will refer to as ∠3) is labeled as 28°.
### Angle Relationships with Parallel Lines
1. **Corresponding Angles:** If a transversal intersects two parallel lines, then each pair of corresponding angles is congruent.
2. **Alternate Interior Angles:** If a transversal intersects two parallel lines, then each pair of alternate interior angles is congruent.
3. **Same-Side Interior Angles:** If a transversal intersects two parallel lines, then each pair of same-side interior angles is supplementary (they add up to 180°).
### Analyzing the Statements
1. **Statement: ∠5 = 28°**
- If ∠5 is located in a position corresponding to ∠3 (say it is in the same position on the opposite side of the transversal), the statement is **True**.
- If ∠5 is an alternate interior angle to ∠3, then it must also be equal to 28°, thus making this statement **True** as well.
2. **Statement: ∠6 = 28°**
- If ∠6 is positioned such that it is a corresponding angle to ∠3, then this statement is also **True**.
- If it is an alternate exterior angle or located in a similar position to ∠3, it will still remain equal to 28°, making this statement **True** as well.
### Summary Table
| Statement | True | False | Reason |
|--------------------|------|-------|--------|
| ∠5 = 28° | True | | Corresponding angles are equal (if ∠5 is in corresponding position). |
| ∠6 = 28° | True | | Alternate interior angles are equal (if ∠6 is alternate interior). |
### Final Truth Value
For the provided statements, both ∠5 and ∠6 are equal to 28°, assuming they follow the rules of corresponding or alternate angles in relation to the parallel lines and the given angle of 28°.
Given:
- Lines A and B are parallel.
- One angle (which we will refer to as ∠3) is labeled as 28°.
### Angle Relationships with Parallel Lines
1. **Corresponding Angles:** If a transversal intersects two parallel lines, then each pair of corresponding angles is congruent.
2. **Alternate Interior Angles:** If a transversal intersects two parallel lines, then each pair of alternate interior angles is congruent.
3. **Same-Side Interior Angles:** If a transversal intersects two parallel lines, then each pair of same-side interior angles is supplementary (they add up to 180°).
### Analyzing the Statements
1. **Statement: ∠5 = 28°**
- If ∠5 is located in a position corresponding to ∠3 (say it is in the same position on the opposite side of the transversal), the statement is **True**.
- If ∠5 is an alternate interior angle to ∠3, then it must also be equal to 28°, thus making this statement **True** as well.
2. **Statement: ∠6 = 28°**
- If ∠6 is positioned such that it is a corresponding angle to ∠3, then this statement is also **True**.
- If it is an alternate exterior angle or located in a similar position to ∠3, it will still remain equal to 28°, making this statement **True** as well.
### Summary Table
| Statement | True | False | Reason |
|--------------------|------|-------|--------|
| ∠5 = 28° | True | | Corresponding angles are equal (if ∠5 is in corresponding position). |
| ∠6 = 28° | True | | Alternate interior angles are equal (if ∠6 is alternate interior). |
### Final Truth Value
For the provided statements, both ∠5 and ∠6 are equal to 28°, assuming they follow the rules of corresponding or alternate angles in relation to the parallel lines and the given angle of 28°.