Payton is working on a proof that consecutive interior angles are supplementary. Given that n ll m, fill in the following 2 column proof.

Question

Statement Reason
1. ∡A + ∡B = 180 Linear pairs are supplementary
2. ∡A = ∡E ________
3. ∡E + ∡C = 180 Substitution
∠E & ∠C are supplementary ________

a. Definition of supplementary angles
b. Vertical Angles Theorem
c. Transitive Property of Equality
d. Corresponding Angles Postulate
e. Substitution
f. Definition of congruence
g. Definition of supplementary angles
h. Linear pairs are supplementary

Answer 1

Here's the completed two-column proof with the appropriate reasons filled in:

| Statement | Reason | |------------------------------------|------------------------------------------------| | 1. ∡A + ∡B = 180 | Linear pairs are supplementary | | 2. ∡A = ∡E | Corresponding Angles Postulate | | 3. ∡E + ∡C = 180 | Substitution | | ∠E & ∠C are supplementary | Definition of supplementary angles |

This logically shows that if n || m, the consecutive interior angles (∠A and ∠C) are indeed supplementary, which is what Payton is trying to prove.