Question

two lines are intersected by a third line. if ∠2 ≅ ∠6, which must be true about ∠2? ∠2 ≅ ∠5 ∠2 is complementary to ∠5. m∠2 = m∠8 ∠2 is supplementary to ∠8.

Explanation:

Step1: Identify angle - pair relationships

When two lines are intersected by a third line (a transversal), $\angle2$ and $\angle6$ are corresponding angles. Given $\angle2\cong\angle6$, the two lines are parallel.

Step2: Analyze $\angle2$ and $\angle8$

$\angle2$ and $\angle8$ are alternate - exterior angles. For parallel lines cut by a transversal, alternate - exterior angles are congruent. So $m\angle2 = m\angle8$.

Step3: Analyze other options

• $\angle2$ and $\angle5$ are neither congruent nor complementary in general for parallel lines cut by a transversal.
• $\angle2$ and $\angle8$ are not supplementary; they are congruent.

Answer:

$m\angle2 = m\angle8$