Question 463932
angle 1 is complement to angle 2
angle 2 is complement to angle 3
prove angle 1 is congruent to angle 3

angle 1 + angle 2 = 90 degrees (definition of complement)
angle 2 + angle 3 = 90 degrees (definition of complement)

angle 1 + angle 2 = angle 2 + angle 3 (substitution)

subtract angle 2 from both sides of the equation.

you are left with angle 1 = angle 3.

the geometric explanation is the subtraction property.

if a = b then a-c = b-c

the a was angle 1 + angle 2 = 90 degrees
the b was angle 2 + angle 3 = 90 degrees

the c was the subtraction of angle 2