prove the acute angles on a right triangle are complementary

Question

GIVEN: triangle ABC with right angle C

Answer 1

Complementary angles are two angles that add up to 90 degrees.

If angle C is a right angle, then it has a measure of 90 degrees.

The angles in a triangle must sum to 180 degrees. If one angle is already 90 degrees, then the other two angles must sum to 90 degrees since 180- 90 = 90.

So if angle C is 90 degrees, then angle A and B must be complementary because they have to add up to 90 degrees.

Hope that helps!