Complementary Angles

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°
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°). Here are two memory aids:

• The phrase "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.
• Put a vertical line on the right of the letter 'c' in 'complementary' to make into a '9'. Complementary angles add to 90.
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