Question

Two lines are intersected by a third line.

Two horizontal parallel lines are intersected by a third line. The third line intersects the top line and forms 4 angles. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. The third line intersects the bottom line and forms 4 angles. Labeled clockwise, from uppercase left, the angles are 5, 6, 8, 7.
If Angle2 Is-congruent-to Angle6, which must be true about Angle2?

Angle2 Is-congruent-to Angle5
Angle2 is complementary to Angle5.
mAngle2 = mAngle8
Angle2 is supplementary to Angle8.

Answer 1

Angle 6 and angle 8 are a linear pair at the bottom intersection, so m∠6 + m∠8 = 180°. Since ∠2 ≅ ∠6, m∠2 = m∠6, hence m∠2 + m∠8 = 180°. Therefore ∠2 is supplementary to ∠8.