Question

Lines v and w are parallel. Which statement can you NOT deduce from this information?

m∠2+m∠5=180
m∠3+m∠8=180
∠4-∠7
∠1=∠8

Answer 1

Based on the rules for vertical angles, ∠1 = ∠4, and ∠5 = ∠8. Based on the rules for corresponding angles, ∠1 = ∠5, so all four of those angles are equivalent.
Similarly, ∠2 = ∠3 = ∠6 = ∠7.
Since ∠2 = ∠6, and ∠5 + ∠6 = 180 degrees, then the first statement is true.
The second statement is also true since ∠3 = ∠7, and ∠7 + ∠8 = 180.
The third statement is false, as it cannot be verified.
The fourth statement is true, as proven in the first part based on vertical and corresponding angles.