Question
In the figure, one angle is labeled 28° , and lines A and B are parallel. Complete the table. For each statement, select True or False. Show your work.
Answers
GPT-4o mini
To complete the table regarding the given figure with lines A and B being parallel and one angle labeled 28°, we will need to apply the properties of angles formed by parallel lines cut by a transversal. Here are some key concepts:
1. **Corresponding Angles:** When a transversal intersects two parallel lines, the angles in the same relative position at each intersection are called corresponding angles. They are equal.
2. **Alternate Interior Angles:** These angles are located on opposite sides of the transversal but within the two parallel lines. They are also equal when the lines are parallel.
3. **Consecutive Interior Angles:** These angles are on the same side of the transversal and inside the parallel lines. They are supplementary (they add up to 180°).
Now, without the actual figure, I will provide a general method to complete your table. Let's assume the labeled angle (28°) is an interior angle formed by a transversal intersecting lines A and B.
### Completing the Table:
Let's say the angle labeled 28° is one of the alternate interior angles. Below is how we might fill out the true/false table based on angle relationships:
1. **Angle A = 28°**
- Statement: "Angle A is equal to the angle opposite to it."
- **Answer:** True (Since they are corresponding angles).
2. **Angle B = 28°**
- Statement: "Angle B is an alternate interior angle."
- **Answer:** True (If it's situated on the opposite side of the transversal and between the two parallel lines).
3. **Angle C = 152°**
- Statement: "Angle C is supplementary to angle A."
- **Answer:** True (If angle A is 28°, then angle C which is on the same side of the transversal and inside the lines will be 180° - 28° = 152°).
4. **Angle D = 180° - 28°**
- Statement: "Angle D and angle A are supplementary."
- **Answer:** True (If angle D is on the same side of the transversal, it could be the angle that adds up to 180° with angle A).
5. **Angle E = 28°**
- Statement: "Angle E is a corresponding angle to angle A."
- **Answer:** True (Corresponding angles are equal).
### Conclusion:
Fill in the true or false answer based on the relationships of the angles you have in your table. If you provide the exact angle placements in the figure, I can deliver a more precise and tailored answer.
1. **Corresponding Angles:** When a transversal intersects two parallel lines, the angles in the same relative position at each intersection are called corresponding angles. They are equal.
2. **Alternate Interior Angles:** These angles are located on opposite sides of the transversal but within the two parallel lines. They are also equal when the lines are parallel.
3. **Consecutive Interior Angles:** These angles are on the same side of the transversal and inside the parallel lines. They are supplementary (they add up to 180°).
Now, without the actual figure, I will provide a general method to complete your table. Let's assume the labeled angle (28°) is an interior angle formed by a transversal intersecting lines A and B.
### Completing the Table:
Let's say the angle labeled 28° is one of the alternate interior angles. Below is how we might fill out the true/false table based on angle relationships:
1. **Angle A = 28°**
- Statement: "Angle A is equal to the angle opposite to it."
- **Answer:** True (Since they are corresponding angles).
2. **Angle B = 28°**
- Statement: "Angle B is an alternate interior angle."
- **Answer:** True (If it's situated on the opposite side of the transversal and between the two parallel lines).
3. **Angle C = 152°**
- Statement: "Angle C is supplementary to angle A."
- **Answer:** True (If angle A is 28°, then angle C which is on the same side of the transversal and inside the lines will be 180° - 28° = 152°).
4. **Angle D = 180° - 28°**
- Statement: "Angle D and angle A are supplementary."
- **Answer:** True (If angle D is on the same side of the transversal, it could be the angle that adds up to 180° with angle A).
5. **Angle E = 28°**
- Statement: "Angle E is a corresponding angle to angle A."
- **Answer:** True (Corresponding angles are equal).
### Conclusion:
Fill in the true or false answer based on the relationships of the angles you have in your table. If you provide the exact angle placements in the figure, I can deliver a more precise and tailored answer.