Answer:
m<GKH + m<HKI = 180; m<HKI + m<IKJ = 180 - Angles forming a linear pair sum to 180
m<GKH + m<HKI = m<HKI + m<IKJ - Subsitution
m<GKH = m<IKJ - Algebra
<GKH ≅ <IKJ - Definition of congruence
Explanation:
Angles that form a linear pair are supplementary because together they make a straight line. So, they must sum to 180.
In statement 2, m<HKI + m<IKJ replaces 180 degrees. This is allowed because m<HKI + m<IKJ is equivalent to 180 degrees, so it can be substituted.
In statement 3, m<HKI is subtracted from both sides. This is allowed through the property of equality, which is a part of algebra.
The definition of congruency is that two shapes that are equal are congruent. So if m<GKH = m<IKJ, then they must be congruent as well.