Question

complete the sentence.
∠4 and ∠8 are corresponding angles.
look for an angle in the same relative position as ∠4.
what are all the angles in the figure that are congruent to ∠2?
∠1, ∠7, ∠8
∠3, ∠5, ∠8
∠3, ∠6, ∠7
∠4, ∠6, ∠8

Explanation:

Step1: Recall the concept of corresponding angles

Corresponding angles are in the same relative position.

Step2: Identify the corresponding angle of ∠4

By observing the figure, ∠8 is in the same relative position as ∠4.

Step3: Recall the concept of congruent angles

Congruent angles have equal measures.

Step4: Find angles congruent to ∠2

Vertical angles: ∠2 and ∠4 are vertical angles ($\angle2=\angle4$). Alternate - interior angles: If we assume the lines are parallel (implied by the angle - relationship context), ∠2 and ∠6 are alternate - interior angles ($\angle2 = \angle6$). Also, ∠6 and ∠8 are vertical angles ($\angle6=\angle8$), so $\angle2=\angle8$. ∠2 and ∠7: If lines are parallel, ∠2 and ∠7 are alternate - exterior angles ($\angle2=\angle7$)

Answer:

$\angle4$ and $\angle8$ are corresponding angles. All angles congruent to $\angle2$ are $\angle4,\angle6,\angle8$