Question
2 lines intersect. A line with points R, S, U intersects a line with points V, S, T at point S.
In the diagram, which angles form a linear pair? Select three options.
AngleRST and AngleRSV
AngleRST and AngleTSU
AngleRST and AngleVSU
AngleTSU and AngleUSV
AngleTSU and AngleRSV
In the diagram, which angles form a linear pair? Select three options.
AngleRST and AngleRSV
AngleRST and AngleTSU
AngleRST and AngleVSU
AngleTSU and AngleUSV
AngleTSU and AngleRSV
Answers
GPT-4o mini
To determine which angles form a linear pair, we need to look for pairs of angles that are adjacent and whose measures add up to 180 degrees.
1. **Angle RST and Angle RSV**: These angles share vertex S and the arms SR and SV. They are adjacent angles formed by the intersection of lines RS and SV. They form a linear pair.
2. **Angle RST and Angle TSU**: Angle RST is not adjacent to Angle TSU, as they are not formed by the same intersection, so they do not form a linear pair.
3. **Angle RST and Angle VSU**: Angle RST is not adjacent to Angle VSU, considering the positions of the points. They do not form a linear pair.
4. **Angle TSU and Angle USV**: These angles share vertex S and the arms SU and SV. They are adjacent and thus form a linear pair.
5. **Angle TSU and Angle RSV**: These angles are not adjacent since they are formed from separate intersections. They do not form a linear pair.
Based on this reasoning, the correct options for angles that form a linear pair are:
- Angle RST and Angle RSV
- Angle TSU and Angle USV
Since the question asks for three options, it seems like there might be a need to clarify whether those two listed would suffice or if there's an additional angle pair you're considering. Please double-check the relationships of the angles mentioned in the options you have provided.
In summary, the confirmed angles forming linear pairs according to standard intersection rules would be:
1. Angle RST and Angle RSV
2. Angle TSU and Angle USV
You may want to confirm if there’s a third that fits the criteria listed in the options. If any additional context or relationships are provided with the angles given, please adjust the evaluation accordingly.
1. **Angle RST and Angle RSV**: These angles share vertex S and the arms SR and SV. They are adjacent angles formed by the intersection of lines RS and SV. They form a linear pair.
2. **Angle RST and Angle TSU**: Angle RST is not adjacent to Angle TSU, as they are not formed by the same intersection, so they do not form a linear pair.
3. **Angle RST and Angle VSU**: Angle RST is not adjacent to Angle VSU, considering the positions of the points. They do not form a linear pair.
4. **Angle TSU and Angle USV**: These angles share vertex S and the arms SU and SV. They are adjacent and thus form a linear pair.
5. **Angle TSU and Angle RSV**: These angles are not adjacent since they are formed from separate intersections. They do not form a linear pair.
Based on this reasoning, the correct options for angles that form a linear pair are:
- Angle RST and Angle RSV
- Angle TSU and Angle USV
Since the question asks for three options, it seems like there might be a need to clarify whether those two listed would suffice or if there's an additional angle pair you're considering. Please double-check the relationships of the angles mentioned in the options you have provided.
In summary, the confirmed angles forming linear pairs according to standard intersection rules would be:
1. Angle RST and Angle RSV
2. Angle TSU and Angle USV
You may want to confirm if there’s a third that fits the criteria listed in the options. If any additional context or relationships are provided with the angles given, please adjust the evaluation accordingly.