Answer:
1. Given.
2. Definition of a linear pair.
3. Given.
4. Congruent Supplements Theorem.
Explanation:
Statement 1
∠JKM and ∠MKL form a linear pair.
Reason: Given
Statement 2
∠JKM and ∠MKL are supplementary
Reason: Definition of supplementary angles.
A linear pair is a pair of adjacent, supplementary angles.
If ∠JKM and ∠MKL form a linear pair then they are supplementary by definition.
Statement 3
∠JKM and ∠LKN are supplementary.
Reason: Given.
Statement 4
∠MKL ≅ ∠LKN
Reason: Congruent Supplements Theorem.
If two angles are supplements of the same angle, then the two angles are congruent.
As ∠MKL and ∠LKN are both supplementary to ∠JKM then ∠MKL and ∠LKN are congruent.