Question

Parallel lines r and s are cut by two transversals, parallel lines t and u.

Lines r and s are crossed by lines t and u to form 16 angles. Clockwise from top left, at the intersection of r and t, the angles are 1, 2, 3, 4; at the intersection of s and t, 5, 6, 7, 8; at the intersection of u and s, 9, 10, 11, 12; at the intersection of u and r, 13, 14, 15, 16.

Which angles are corresponding angles with angle 8?
Angle4 and Angle12
Angle2 and Angle10
Angle6 and Angle14
Angle3 and Angle9

Answer 1

To identify the pairs of corresponding angles, we need to recall that corresponding angles are formed when two parallel lines are crossed by a transversal. Corresponding angles are located in the same relative position at each intersection.

In this scenario, the lines r and s are parallel, and lines t and u are the transversals. Let's label the angles based on the given intersections:

- At the intersection of r and t:
- Angle 1 (top left, clockwise)
- Angle 2 (top right)
- Angle 3 (bottom right)
- Angle 4 (bottom left)

- At the intersection of s and t:
- Angle 5 (top left)
- Angle 6 (top right)
- Angle 7 (bottom right)
- Angle 8 (bottom left)

- At the intersection of u and s:
- Angle 9 (top left)
- Angle 10 (top right)
- Angle 11 (bottom right)
- Angle 12 (bottom left)

- At the intersection of u and r:
- Angle 13 (top left)
- Angle 14 (top right)
- Angle 15 (bottom right)
- Angle 16 (bottom left)

Now, we wish to find the angles that are corresponding to angle 8 (which is located at the intersection of s and t).

Since angle 8 is located at the bottom left of intersection s and t, we need to find the angle that is also at the bottom left position at another intersection.

1. At the intersection of r and t, the bottom left angle is angle 4.
2. At the intersection of u and s, the bottom left angle is angle 12.
3. At the intersection of u and r, the bottom left angle is angle 16.

Thus:
- Angle 4 corresponds to angle 8
- Angle 12 corresponds to angle 8

From the options provided:
- **Angle 4 and Angle 12** are both the corresponding angles with angle 8.

So, the answer is:
**Angle 4 and Angle 12**.