If two angles are complementary and one angle is 10 degree

Two angles are Complementary when they
add up to 90 degrees (a Right Angle

These two angles (40° and 50°) are Complementary Angles, because they add up to 90°:

Notice that together they make a right angle

But the angles don't have to be together.

These two are complementary because 27° + 63° = 90°

(Drag the points)

images/geom-comp-supp.js?mode=comp

Right Angled Triangle

In a right angled triangle, the two non-right angles are complementary, because in a triangle the three angles add to 180°, and 90° has already been taken by the right angle.

When two angles add to 90°, we say they "Complement" each other.

Complementary comes from Latin completum meaning "completed" ...
because the right angle is thought of as being a complete angle.

Spelling: be careful, it is not "Complimentary Angle" (with an "i") ...
that would be an angle you get for free!

Complementary vs Supplementary

A related idea is Supplementary Angles - those add up to 180°

How to remember which is which? Well, alphabetically they are:

• Complementary add to 90°
• Supplementary add to 180°

You can also think:

• "C" of Complementary is for "Corner" (a Right Angle), and
• "S" of Supplementary is for "Straight" (180° is a straight line)

Or you can think:

• when you are right you get a compliment (sounds like complement)
• "supplement" (like a vitamin supplement) is something extra, so is bigger

5231, 5233, 819, 2109, 820, 2110, 5240, 9063, 3305, 3306