Question

Transversal t intersects lines d and e to form 8 angles. The angles formed with line d, clockwise from top left are 1, 2, 7, 8. The angles formed with line e, clockwise from top left are 3, 4, 5, 6.
Which angle is an alternate exterior angle to ∠8?
∠3
∠4
∠5
∠6

Answer 1

To determine which angle is an alternate exterior angle to ∠8, we first need to understand the arrangement of the angles formed by the transversal \( t \) intersecting lines \( d \) and \( e \).

The angles formed by the transversal with line \( d \) from the top left are:
- ∠1, ∠2 (top angles with line \( d \))
- ∠7, ∠8 (bottom angles with line \( d \))

The angles formed by the transversal with line \( e \) from the top left are:
- ∠3, ∠4 (top angles with line \( e \))
- ∠5, ∠6 (bottom angles with line \( e \))

Since vertical angles are equal and adjacent angles are supplementary, we will focus on identifying the relationship of the angles.

Alternate exterior angles are pairs of angles that are on opposite sides of the transversal and are outside the two lines.

From the arrangement:
- ∠8 is located at the bottom right of line \( d \).
- The exterior angles that alternate with ∠8, located outside the two lines, are ∠3 (which is located at the top left of line \( e \)).

Therefore, the alternate exterior angle to ∠8 is ∠3.

Thus, the answer is:

**∠3**