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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 $∠ 1$ and $∠ 2$ form a right angle. According to theorem, the following equation holds true.

$m ∠ 1 + m ∠ 2 = 9 0^{\circ}$

Proof

Consider angles $∠ 1$ and $∠ 2$ shown in the diagram. Here, their non-common sides form a right angle.

Since the measure of

∠ A B C

9 0^{\circ},

by the Angle Addition Postulate, the sum of the measures of

∠ 1

and

∠ 2

9 0^{\circ} .

m ∠ 1 + m ∠ 2 = m ∠ A B C ⇓ m ∠ 1 + m ∠ 2 = 9 0^{\circ}

The above equation implies that

∠ 1

and

∠ 2

are complementary angles.

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Proof