Question

Transversal r intersects lines p and q to form 8 angles. The angles formed with line p, clockwise from top left are 1, 5, 6, 2. The angles formed with line q, clockwise from top left are 3, 7, 8, 4.
Which angles are corresponding angles? Select all that apply.
∠1 and ∠3
∠6 and ∠8
∠2 and ∠8
∠5 and ∠7
∠2 and ∠7
∠3 and ∠6

Answer 1

To identify the corresponding angles formed by the transversal \( r \) intersecting lines \( p \) and \( q \), we need to understand the positioning of the angles. Corresponding angles are located in the same relative position at each intersection formed by a transversal and two parallel lines.

The angles formed with line \( p \) are labeled as:
- \( \angle 1 \) (top left)
- \( \angle 5 \) (bottom left)
- \( \angle 6 \) (bottom right)
- \( \angle 2 \) (top right)

The angles formed with line \( q \) are labeled as:
- \( \angle 3 \) (top left)
- \( \angle 7 \) (bottom left)
- \( \angle 8 \) (bottom right)
- \( \angle 4 \) (top right)

Now let's match the angles based on their positions:

- \( \angle 1 \) (top left with \( p \)) corresponds to \( \angle 3 \) (top left with \( q \)): **Corresponding angles**
- \( \angle 5 \) (bottom left with \( p \)) corresponds to \( \angle 7 \) (bottom left with \( q \)): **Corresponding angles**
- \( \angle 6 \) (bottom right with \( p \)) corresponds to \( \angle 8 \) (bottom right with \( q \)): **Corresponding angles**
- \( \angle 2 \) (top right with \( p \)) corresponds to \( \angle 4 \) (top right with \( q \)): **Corresponding angles**

Now, let's see which pairs from your options are indeed corresponding angles:

- \( \angle 1 \) and \( \angle 3 \) → **Yes**
- \( \angle 6 \) and \( \angle 8 \) → **Yes**
- \( \angle 2 \) and \( \angle 8 \) → **No**
- \( \angle 5 \) and \( \angle 7 \) → **Yes**
- \( \angle 2 \) and \( \angle 7 \) → **No**
- \( \angle 3 \) and \( \angle 6 \) → **No**

Thus, the angles that are corresponding angles are:
- \( \angle 1 \) and \( \angle 3 \)
- \( \angle 6 \) and \( \angle 8 \)
- \( \angle 5 \) and \( \angle 7 \)