Complementary Angles
From Latin: complementum - "that which fills up or completes"
Definition: Two angles that add up to 90°
Try this Drag an orange dot. The two angles will change so that they always add to 90°
(If there is no image below, see support page.)
In the figure above, the two angles ∠PQR and
∠JKL are complementary because they always add to 90°
Often the two angles are
adjacent, in which case they form a
right angle.
In a
right triangle, the two smaller angles are always complementary.
(Why? - one angle is 90° and all three add up to 180°.
Therefore the two smaller ones must add to 90° and so are complementary by definition).
See the page on right triangles
and convince yourself that this is true.
Similar in concept are supplementary angles, which add up to 180°.
A way to remember
Sometimes it's hard to remember which is which between supplementary (adds to 180°) and complementary (adds to 90°).
One phrase that may help is "it's right to give compliments"
A right angle is 90 degrees and, yes, 'compliment' and 'complement' are not the same word, but it's a way to remember which is which.
Related angle topics
General
Angle Types
Angle relationships
(C) 2007 Copyright John Page
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