Question
A section of wall is being framed. A model of the framing work is shown below.
Vertical and parallel lines c, d, and e are cut by diagonal transversal b. The uppercase right angle formed by the intersection of lines b and c is angle A. The uppercase left angle formed by the intersection of lines d and b is 125 degrees.
Which best describes the relationship between the 125° angle and angle A?
They are same side interior angles. Angle A measures 55°.
They are alternate interior angles. Angle A measures 125°.
They are vertical angles. Angle A measures 125°.
They are corresponding angles. Angle A measures 55°.
Vertical and parallel lines c, d, and e are cut by diagonal transversal b. The uppercase right angle formed by the intersection of lines b and c is angle A. The uppercase left angle formed by the intersection of lines d and b is 125 degrees.
Which best describes the relationship between the 125° angle and angle A?
They are same side interior angles. Angle A measures 55°.
They are alternate interior angles. Angle A measures 125°.
They are vertical angles. Angle A measures 125°.
They are corresponding angles. Angle A measures 55°.
Answers
Answered by
GPT-4o mini
To determine the relationship between the 125° angle and angle A, let's analyze the situation based on the provided information:
1. Angle A is formed by the intersection of line b (the transversal) and line c (a vertical line) at a right angle, which means angle A is 90°.
2. The angle formed at the intersection of line b and line d (another vertical line) is given as 125°.
Now, we can identify the relationships:
- The 125° angle is on the same side of the transversal and inside the two parallel lines (c and d). According to the properties of parallel lines cut by a transversal, these angles are classified as same side interior angles.
- Since angle A is 90°, we determine the measure of angle A is not 125°.
Therefore, the best description of the relationship is that they are same side interior angles, but we should correct the measure of angle A: it is actually 90°, not 55°.
However, among the choices given, it states: "They are same side interior angles. Angle A measures 55°." Since 55° is incorrect, but the relationship stands correct, it's important to note that the angle A actually measures 90°.
In conclusion, the best choice from the options is:
"They are same side interior angles. Angle A measures 55°." (with the understanding that the measurement of angle A given is incorrect).
1. Angle A is formed by the intersection of line b (the transversal) and line c (a vertical line) at a right angle, which means angle A is 90°.
2. The angle formed at the intersection of line b and line d (another vertical line) is given as 125°.
Now, we can identify the relationships:
- The 125° angle is on the same side of the transversal and inside the two parallel lines (c and d). According to the properties of parallel lines cut by a transversal, these angles are classified as same side interior angles.
- Since angle A is 90°, we determine the measure of angle A is not 125°.
Therefore, the best description of the relationship is that they are same side interior angles, but we should correct the measure of angle A: it is actually 90°, not 55°.
However, among the choices given, it states: "They are same side interior angles. Angle A measures 55°." Since 55° is incorrect, but the relationship stands correct, it's important to note that the angle A actually measures 90°.
In conclusion, the best choice from the options is:
"They are same side interior angles. Angle A measures 55°." (with the understanding that the measurement of angle A given is incorrect).
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