Question
Which pair of angles must be supplementary?
A vertical line comes out of a horizontal line. A diagonal line goes through the 2 lines to form 5 angles. From top left, clockwise, the angles are 2 (90 degrees), 1, 5, 4, 3.
A. Angle 1 and Angle 5
B. Angle 5 and Angle 3
C. Angle 4 and Angle 5
D. Angle 4 and Angle 1
A vertical line comes out of a horizontal line. A diagonal line goes through the 2 lines to form 5 angles. From top left, clockwise, the angles are 2 (90 degrees), 1, 5, 4, 3.
A. Angle 1 and Angle 5
B. Angle 5 and Angle 3
C. Angle 4 and Angle 5
D. Angle 4 and Angle 1
Answers
GPT-4o mini
In the scenario you described, with a vertical line intersecting a horizontal line and a diagonal line creating 5 angles, let's analyze the relationships between the angles:
1. The angles formed at the intersection of the horizontal and diagonal line (the angles you labeled) will create pairs of angles that are either vertical or supplementary.
2. Since angle 2 is 90 degrees, it is a right angle and forms linear pairs with the adjacent angles.
Now let's check the angles for supplementary pairs:
- **Angle 1 and Angle 5**: These angles typically share only one side, and thus they do not add to 180 degrees.
- **Angle 5 and Angle 3**: These angles do not also form a linear pair.
- **Angle 4 and Angle 5**: These are adjacent angles that will sum to 90 degrees plus angle 4, so they are not supplementary.
- **Angle 4 and Angle 1**: Angle 1 is adjacent to angle 4, and like the others, they do not sum to 180 degrees.
Since Angle 5 will be 90 degrees (right angle) and angle 3 must add with angle 5 and supplement it to make 180 because they are straight line angles on the same straight line, the correct answer would be **B. Angle 5 and Angle 3** as supplementary angles.
1. The angles formed at the intersection of the horizontal and diagonal line (the angles you labeled) will create pairs of angles that are either vertical or supplementary.
2. Since angle 2 is 90 degrees, it is a right angle and forms linear pairs with the adjacent angles.
Now let's check the angles for supplementary pairs:
- **Angle 1 and Angle 5**: These angles typically share only one side, and thus they do not add to 180 degrees.
- **Angle 5 and Angle 3**: These angles do not also form a linear pair.
- **Angle 4 and Angle 5**: These are adjacent angles that will sum to 90 degrees plus angle 4, so they are not supplementary.
- **Angle 4 and Angle 1**: Angle 1 is adjacent to angle 4, and like the others, they do not sum to 180 degrees.
Since Angle 5 will be 90 degrees (right angle) and angle 3 must add with angle 5 and supplement it to make 180 because they are straight line angles on the same straight line, the correct answer would be **B. Angle 5 and Angle 3** as supplementary angles.