Question

∠2≅∠4
∠4≅∠8
∠6 + ∠7 = 180°
∠3 + ∠4 = 180°

Explanation:

Step1: Recall angle - pair relationships

Vertical angles are congruent. Linear - pair angles are supplementary.

Step2: Analyze each option

• $\angle2$ and $\angle4$ are vertical angles, so $\angle2\cong\angle4$.
• $\angle4$ and $\angle8$ are corresponding angles if $u\parallel v$, but we are not given $u\parallel v$.
• $\angle6$ and $\angle7$ are vertical angles, so $\angle6+\angle7

eq180^{\circ}$.

• $\angle3$ and $\angle4$ are vertical angles, so $\angle3+\angle4

eq180^{\circ}$.

Answer:

$\angle2\cong\angle4$