Question

the figure shows a transversal that intersects two parallel lines. none of the angles are right angles.
complete the sentence.
∠4 and ∠8 are corresponding angles.
what are all the angles in the figure that are congruent to ∠2?
options: ∠1, ∠7, ∠8; ∠3, ∠5, ∠8; ∠3, ∠6, ∠7; ∠4, ∠6, ∠8

Explanation:

Step1: Identify corresponding angles

Corresponding angles are in matching positions relative to the parallel lines and transversal. $\angle4$ is on the lower right of the first intersection, so its corresponding angle is $\angle8$ (lower right of the second intersection).

Step2: Find angles congruent to $\angle2$

1. Vertical angles: $\angle2$ and $\angle4$ are vertical angles, so $\angle2 \cong \angle4$.
2. Corresponding angles: $\angle2$ corresponds to $\angle6$, so $\angle2 \cong \angle6$.
3. Vertical angles to corresponding angle: $\angle6$ and $\angle8$ are vertical angles, so $\angle6 \cong \angle8$, meaning $\angle2 \cong \angle8$.

Answer:

1. $\angle 8$
2. $\angle 4, \angle 6, \angle 8$