Question

A conjecture and the paragraph proof used to prove the conjecture are shown.

Answer 1

∠1 and ​ ∠2 ​ form a linear pair, so ∠1 and ∠2 are supplementary by the LINEAR PAIR POSTULATE . Therefore, m∠1 + m∠2 = 180° by the definition of supplementary. It is given that ∠2 ≅ ∠3 so m∠2 = m∠3 by the ANGLE CONGRUENCE POSTULATE . By substitution, m∠1 + m∠3 = 180°, so ∠1 and ∠3 are supplementary by the definition of supplementary.

Answer 2

1. Linear Pair Postulate
2. MAngle 3
3.Angle 3
4.Angle Congruence Postulate

Hope this helps!
-Soul