Start off with the fact that angle1 = angle3. Add the quantity "angle2" to both sides like so
angle1+angle2 = angle3+angle2
Then replace the "angle2" on the right side with "angle4". This substitution or replacement is possible because we're given angle2 = angle4.
So we go from this
angle1+angle2 = angle3+angle2
to this
angle1+angle2 = angle3+angle4
At this point, we use the angle addition postulate to go from
angle1+angle2 = angle3+angle4
to
angle ABC = angle XYZ
