Question
Lines p and q are parallel.
Parallel lines p and q are cut by transversals r and s. At the intersection of lines p, r, and s, clockwise from top left, the angles are blank, 93 degrees, blank, blank, 1, 60 degrees. At the intersection of lines q and s, the angles are blank, 2, blank, blank. At the intersection of r and q, the angles are 3, blank, blank, blank.
What is the measure of angle 3 in degrees?
27°
33°
60°
153°
Parallel lines p and q are cut by transversals r and s. At the intersection of lines p, r, and s, clockwise from top left, the angles are blank, 93 degrees, blank, blank, 1, 60 degrees. At the intersection of lines q and s, the angles are blank, 2, blank, blank. At the intersection of r and q, the angles are 3, blank, blank, blank.
What is the measure of angle 3 in degrees?
27°
33°
60°
153°
Answers
GPT-4o mini
To solve this problem, we will use the information given about the angles formed by parallel lines and transversals.
1. **At the intersection of lines p, r, and s, we know the angles:**
- Top left angle: blank
- Top right angle: 93°
- Bottom left angle: blank
- Bottom right angle: blank
- Bottom left angle (at the intersection of lines p and r): 1 (assumed to be in degrees)
- Bottom right angle (at the intersection of lines p and s): 60°.
Since lines p and q are parallel:
- The angle adjacent to the 93° angle (the bottom right angle at intersection of p and r) is also 93° (because they are corresponding angles).
- The angle adjacent to 60° (which is vertical to angle at r and q) should also be 60° because they are vertical angles.
From the angles at the intersection of lines p, r, and s, we can deduce the angles:
- The angle adjacent to the 93° angle at the bottom left is \( 180° - 93° = 87° \).
- For the top left angle, it is the angle supplementary to angle 1 (which has not been defined), but we will follow another method to find angle 3 without needing to know angle 1.
2. **At the intersection of lines q and s:**
- Top left: blank
- Top right: 2 (in degrees)
- Bottom left: blank
- Bottom right: blank.
Since lines p and q are parallel:
- The angle on line q corresponding to the 60° angle above at p is 60°.
- Therefore, from corresponding angles and vertically opposite angles, we can set up:
- \( 2 = 60° \) hence angle at that intersection should be \( 180 - 60 = 120° \) (which is the blank or adjacent angle to angle labelled 2).
From the angle settings:
- Hence, we deduce that angle \( 3 \) should be equal to \( 120° \) because of the transversal behavior with respect to the angle settings of q and r.
3. **Most crucial step – Calculate angle 3:**
- Since angle 3 can be calculated by the adjacent angle above being equal to angle at p formed by transversal relationship and translating vertical angles:
Based on reasoning and solving parallel geometry, we finalize:
- The measure of angle 3 as \( 180° - 120° = 60° \).
**Conclusion**:
Hence, the correct answer is \( 60° \).
1. **At the intersection of lines p, r, and s, we know the angles:**
- Top left angle: blank
- Top right angle: 93°
- Bottom left angle: blank
- Bottom right angle: blank
- Bottom left angle (at the intersection of lines p and r): 1 (assumed to be in degrees)
- Bottom right angle (at the intersection of lines p and s): 60°.
Since lines p and q are parallel:
- The angle adjacent to the 93° angle (the bottom right angle at intersection of p and r) is also 93° (because they are corresponding angles).
- The angle adjacent to 60° (which is vertical to angle at r and q) should also be 60° because they are vertical angles.
From the angles at the intersection of lines p, r, and s, we can deduce the angles:
- The angle adjacent to the 93° angle at the bottom left is \( 180° - 93° = 87° \).
- For the top left angle, it is the angle supplementary to angle 1 (which has not been defined), but we will follow another method to find angle 3 without needing to know angle 1.
2. **At the intersection of lines q and s:**
- Top left: blank
- Top right: 2 (in degrees)
- Bottom left: blank
- Bottom right: blank.
Since lines p and q are parallel:
- The angle on line q corresponding to the 60° angle above at p is 60°.
- Therefore, from corresponding angles and vertically opposite angles, we can set up:
- \( 2 = 60° \) hence angle at that intersection should be \( 180 - 60 = 120° \) (which is the blank or adjacent angle to angle labelled 2).
From the angle settings:
- Hence, we deduce that angle \( 3 \) should be equal to \( 120° \) because of the transversal behavior with respect to the angle settings of q and r.
3. **Most crucial step – Calculate angle 3:**
- Since angle 3 can be calculated by the adjacent angle above being equal to angle at p formed by transversal relationship and translating vertical angles:
Based on reasoning and solving parallel geometry, we finalize:
- The measure of angle 3 as \( 180° - 120° = 60° \).
**Conclusion**:
Hence, the correct answer is \( 60° \).