Question

which congruence sentences represent congruent alternate exterior angles? ∠1 ≅ ∠8 and ∠2 ≅ ∠7 ∠3 ≅ ∠6 and ∠4 ≅ ∠5 ∠1 ≅ ∠5 and ∠2 ≅ ∠6 ∠1 ≅ ∠4 and ∠2 ≅ ∠3

Explanation:

Step1: Recall Alternate Exterior Angles Definition

Alternate exterior angles are non - adjacent angles that lie outside the two parallel lines and on opposite sides of the transversal.

Step2: Identify Exterior Angles

For the two parallel lines (the horizontal lines) and the transversal (the slanted line), the exterior angles are $\angle 1$, $\angle 2$, $\angle 7$, $\angle 8$.

Step3: Check Alternate Exterior Angle Pairs

• $\angle 1$ and $\angle 8$: $\angle 1$ is above the top parallel line and to the left of the transversal, $\angle 8$ is below the bottom parallel line and to the right of the transversal. They are alternate exterior angles.
• $\angle 2$ and $\angle 7$: $\angle 2$ is above the top parallel line and to the right of the transversal, $\angle 7$ is below the bottom parallel line and to the left of the transversal. They are alternate exterior angles.

The other options:

• $\angle 3 \cong \angle 6$ and $\angle 4 \cong \angle 5$ are alternate interior angles.
• $\angle 1 \cong \angle 5$ and $\angle 2 \cong \angle 6$ are corresponding angles.
• $\angle 1 \cong \angle 4$ and $\angle 2 \cong \angle 3$ are vertical angles.

Answer:

$\boldsymbol{\angle 1 \cong \angle 8}$ and $\boldsymbol{\angle 2 \cong \angle 7}$