See below for the proof:

Statements (Reasons)

1) Right ##DeltaABC## with right ##/_C##. ( Given)

2) ##m/_A+m/_B+m/_C=180^@## (Triangle Sum Theorem)

3) ##m/_C=90^@## (Definition of a right angle)

4) ##m/_A+m/_B+90^@=180^@## (Substitution Property of Equality)

5) ##m/_A+m/_B=90^@## (Subtraction Property of Equality)

Note that in step 4 ##90^@## is substituted for ##m/_C## in the step 2 equation since the two things are equal according to step 3.

Note that in step 5 ##90^@## is subtracted from both sides of the step 4 equation.