The proof - ∠ 5 + ∠ 2 + ∠ 6 = 180 - is completed using relevant theorems some includes
- alternate interior angles congruent
How to complete the proof
The two column proof is written as follows
Statement Reason
∠ 1 + ∠ 2 + ∠ 3 = ∠ LAM angle addition postulate
y || Z given
∠1 ≅ ∠ 5 and ∠3 ≅ ∠ 6 alternate interior angles congruent
∠ 1 + ∠ 2 + ∠ 3 = 180 definition of straight angle
∠ 5 + ∠ 2 + ∠ 6 = 180 substitution property of equality