Algebra is number 3 - You have subtracted the measure of angle HKI from the equation.
Transitive property of equality is number 2 - Because both pairs of angles equal 180 degrees, you can set them equal to each other.
Definition of congruence is number 4 - The congruence symbol is in the equation, which tells you that the two angles are congruent.
Angles forming a linear pair sum to 180 degrees is number 1 - 180 degrees is in the equations given and the angles all form linear pairs.
Hope this helps!! :)