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 alternate interior angles with angle 3?
Angle5 and Angle13
Angle7 and Angle15
Angle6 and Angle16
Angle8 and Angle14

Answer 1

To determine which angles are alternate interior angles with angle 3, we first need to understand the arrangement and properties of alternate interior angles formed by two parallel lines (r and s) cut by a pair of transversals (t and u).

1. Angle 3 is located at the intersection of line r and line t.
2. The corresponding alternate interior angle in this configuration will be positioned on the opposite side of the transversal t, with respect to line s.

Now, let's analyze the provided angles based on their positions:

- **Angle 3** is at the top-left intersection (r and t).
- **Angle 5** is at the intersection of line s and line t (above angle 3).
- **Angle 7** is at the intersection of line s and line t (to the right of angle 5).
- **Angle 6** is below angle 5 on the left side of line t.
- **Angle 8** is below angle 7 on the right side of line t.
- **Angle 9** is at the intersection of line u and line s.
- **Angle 10** is to the right of angle 9.
- **Angle 11** is below angle 10 on line u.
- **Angle 12** is below angle 11 on line u.
- **Angle 13** is at the intersection of line u and line r (right of angle 3).
- **Angle 14** is below angle 13 on line u.
- **Angle 15** is below angle 14 on line u.
- **Angle 16** is below angle 15 on line u.

By the properties of alternate interior angles:

- The angles that are alternate interior to angle 3 must be in positions such that they are formed by the same transversal (line t) but under the other parallel line (line s).

Thus:
- **Angle 6** (below angle 5) and **Angle 16** (below angle 15) must be alternate interior angles with angle 3.

Hence, the pairs of angles we analyze:
- **Angle 6 and Angle 16** are alternate interior angles with angle 3.

Therefore, the correct option is:
**Angle 6 and Angle 16.**