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 occupy matching positions at each intersection of the transversal and parallel lines. For $\angle4$, its matching position at the other intersection is $\angle8$.

Step2: Identify angles congruent to $\angle2$

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

Answer:

1. $\angle 4$ and $\boldsymbol{\angle 8}$ are corresponding angles.
2. $\boldsymbol{\angle 4, \angle 6, \angle 8}$