Complementary angles

Diagram

$[asy] import olympiad; size(150); pair D = (0, 10), C = (10, 5), B = (10, 0), A = (0, 0); draw(A--B); draw(C--A); draw(D--A); markscalefactor=0.1; draw(rightanglemark((0,10),(0,0),(10,0))); label("$A$", A, SW); label("$B$", B, SE); label("$C$", C, NE); label("$D$", D, NE); [/asy]$

As long as $\angle BAD$ is a right angle, $\angle BAC$ and $\angle CAD$ are complementary angles to each other.

Definitions

Bing/Google

Either of two angles whose sum is $90^{\circ}$

Merriam-Webster

Two angles that add up to $90$ degrees

Properties and Examples

Property

$\angle A$ is complementary to $\angle B$ if and only if $\angle A + \angle B = 90$ $\text{degrees}$

Examples

If $\angle A$ is $29$ $\text{degrees}$ and $\angle B$ is $61$ $\text{degrees}$ , angle A and angle B are complementary since $29 + 61 = 90$

If $\angle A$ is $30$ $\text{degrees}$ and $\angle B$ is $62$ $\text{degrees}$ , angle A and angle B are not complementary since $30 + 62 = 92$ , and not $90$ $\text{degrees}$ .

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