Question

Which angles are pairs of corresponding angles? Check all that apply.

4 lines intersect to form 16 angles. Clockwise from top left, the angles are 1, 2, 3, 4; 5, 6, 7, 9; 9, 10, 11, 12; 13, 14, 15, 16.
Angle1 and Angle3
Angle2 and Angle14
Angle1 and Angle6
Angle3 and Angle7
Angle8 and Angle9
Angle5 and Angle12

Answer 1

To determine which angles are pairs of corresponding angles, it’s important to recall that corresponding angles are in the same position on parallel lines cut by a transversal.

In the context of the angle arrangement you provided (placed in a grid layout), corresponding angles will occupy similar positions in their respective groups formed by transversal intersections.

Given the angles:
- Quadrant 1: Angles 1, 2, 3, 4
- Quadrant 2: Angles 5, 6, 7, 8
- Quadrant 3: Angles 9, 10, 11, 12
- Quadrant 4: Angles 13, 14, 15, 16

Let's analyze the pairs given:

- **Angle 1 and Angle 3**: **Not corresponding**; they are in the same row.
- **Angle 2 and Angle 14**: **Corresponding**; both are in the second position of rows 1 and 4 respectively.
- **Angle 1 and Angle 6**: **Corresponding**; both are in the first position of rows 1 and 2 respectively.
- **Angle 3 and Angle 7**: **Corresponding**; both are in the third position of rows 1 and 2 respectively.
- **Angle 8 and Angle 9**: **Not corresponding**; they are in different rows.
- **Angle 5 and Angle 12**: **Corresponding**; both are in the first position of rows 2 and 3 respectively.

Thus, the pairs that are corresponding angles are:

1. Angle 2 and Angle 14
2. Angle 1 and Angle 6
3. Angle 3 and Angle 7
4. Angle 5 and Angle 12