In the figure, AB¯¯¯¯¯∥CD¯¯¯¯¯ and m∠2=55°. What is m∠8? Enter your answer in the box.?

m∠2 = 55° (given)
m∠6 = m∠2 = 55° (corresponding angles, AB//CD)
m∠8 = m∠6 = 55° (vertically opposite angles)

The answer filled in the box: 55

55

Angle 2 = Angle 4 (intersecting lines, opposite angles are equal) and
Angle 4 = Angle 8, (intersection parallel lines corresponding angles are equal)
ergo Angle 8 = Angle 2 = 55

Angle 8 is 55 degrees

When a line is crossed by another line, the opposite angles are the same and adjacent angles add to 180.

When parallel lines are crossed by a line, the angles created are the same.

So based on these rules, ∠2 is the same as ∠4, which is the same as ∠8. So ∠8 is also 55°.