Rule

Complement Theorem

If the non-common sides of two adjacent angles form a right angle, then the angles are complementary angles.
Two adjacent angles forming a right angle

As can bee seen, the non-common sides of and form a right angle. According to theorem, the following equation holds true.

Proof

Consider angles and shown in the diagram. Here, their non-common sides form a right angle.

Two adjacent angles forming a right angle
Since the measure of is by the Angle Addition Postulate, the sum of the measures of and is
The above equation implies that and are complementary angles.
Exercises