Question
The lines A and B are parallel. Identify a pair of corresponding angles?
Responses
A ∠1 and ∠6∠1 and ∠6
B ∠3 and ∠8∠3 and ∠8
C ∠6 and ∠5∠6 and ∠5
D ∠5 and ∠7∠5 and ∠7
Question 2
If ∠5 measures 110°, what is the measure of ∠2?
Responses
A 55°55°
B 70°70°
C 110°110°
D 160°
Responses
A ∠1 and ∠6∠1 and ∠6
B ∠3 and ∠8∠3 and ∠8
C ∠6 and ∠5∠6 and ∠5
D ∠5 and ∠7∠5 and ∠7
Question 2
If ∠5 measures 110°, what is the measure of ∠2?
Responses
A 55°55°
B 70°70°
C 110°110°
D 160°
Answers
GPT-4o mini
To answer your questions, let's analyze each one separately.
**Question 1: Identify a pair of corresponding angles.**
When two lines are parallel, corresponding angles are the angles that are in the same position relative to the transversal line. Based on the standard arrangement of angles when two parallel lines are cut by a transversal:
- **∠1 and ∠6** are corresponding angles.
- **∠3 and ∠8** are also corresponding angles.
- **∠5 and ∠7** are corresponding angles.
However, **∠6 and ∠5** are not corresponding since they are on different sides of the transversal.
Thus, the correct responses for corresponding angles are **A (∠1 and ∠6)** or **B (∠3 and ∠8)** or **D (∠5 and ∠7)** depending on the specific diagram you have. If you are looking for a single answer, then the most commonly referenced pairs in such settings are **∠1 and ∠6** or **∠3 and ∠8**.
**Question 2: If ∠5 measures 110°, what is the measure of ∠2?**
If angles 5 and 2 are alternate interior angles formed by the transversal crossing two parallel lines, then they are equal. Therefore, if ∠5 = 110°, then ∠2 also equals 110°.
So, the answer is **C (110°)** if angle 2 is indeed an alternate interior angle to angle 5.
If angle 2 is related to angle 5 in a different way (like being a supplementary angle), we could say that:
- If they are supplementary, then ∠2 = 180° - 110° = 70°.
You need to clarify the relationship based on the diagram provided to determine which case applies.
In conclusion:
- For Question 1, either A, B, or D could be the right answer.
- For Question 2, based on the angle relationships, the answer is **C (110°)** if ∠2 is an alternate angle to ∠5. Otherwise, it's **B (70°)** if they are supplementary.
**Question 1: Identify a pair of corresponding angles.**
When two lines are parallel, corresponding angles are the angles that are in the same position relative to the transversal line. Based on the standard arrangement of angles when two parallel lines are cut by a transversal:
- **∠1 and ∠6** are corresponding angles.
- **∠3 and ∠8** are also corresponding angles.
- **∠5 and ∠7** are corresponding angles.
However, **∠6 and ∠5** are not corresponding since they are on different sides of the transversal.
Thus, the correct responses for corresponding angles are **A (∠1 and ∠6)** or **B (∠3 and ∠8)** or **D (∠5 and ∠7)** depending on the specific diagram you have. If you are looking for a single answer, then the most commonly referenced pairs in such settings are **∠1 and ∠6** or **∠3 and ∠8**.
**Question 2: If ∠5 measures 110°, what is the measure of ∠2?**
If angles 5 and 2 are alternate interior angles formed by the transversal crossing two parallel lines, then they are equal. Therefore, if ∠5 = 110°, then ∠2 also equals 110°.
So, the answer is **C (110°)** if angle 2 is indeed an alternate interior angle to angle 5.
If angle 2 is related to angle 5 in a different way (like being a supplementary angle), we could say that:
- If they are supplementary, then ∠2 = 180° - 110° = 70°.
You need to clarify the relationship based on the diagram provided to determine which case applies.
In conclusion:
- For Question 1, either A, B, or D could be the right answer.
- For Question 2, based on the angle relationships, the answer is **C (110°)** if ∠2 is an alternate angle to ∠5. Otherwise, it's **B (70°)** if they are supplementary.