Download Complementary Angles

Names of Angles
As the Angle Increases, the Name Changes:
Type of Angle
Description
Acute Angle an angle that is less than 90°
Right Angle an angle that is 90° exactly
an angle that is greater than 90° but
Obtuse Angle
less than 180°
Straight Angle an angle that is 180° exactly
Reflex Angle an angle that is greater than 180°
Be Careful What You Measure
This is an Obtuse Angle
And this is a Reflex Angle
But the lines are the same ... so when naming the angles make sure
that you know which angle is being asked for!
Parts of an Angle
The corner point of an angle is called the vertex
And the two straight sides are called arms
The angle is the amount of turn between each arm.
How to Label Angles
There are two main ways to label angles:
1. give the angle a name, usually a lower-case letter like a or
b, or sometimes a Greek letter like α (alpha) or θ (theta)
2. or by the three letters on the shape that define the angle,
with the middle letter being where the angle actually is (its
vertex).
Example angle "a" is "BAC", and angle "θ" is "BCD"
Complementary Angles
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 bec
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.
.
If 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 can you remember which is which? Easy! Think:


"C" of Complementary stands for "Corner"
(a Right Angle), and
"S" of Supplementary stands for "Straight" (180 degrees is a straight line)
Or you can think: when you are right you get a compliment (sounds like complement).
Or you could also think: "Supplement" (like a Vitamin Supplement) is something extra, so it it
bigger.
Supplementary Angles
Two Angles are Supplementary if they add up to 180 degrees.
These two angles (140° and 40°)
are Supplementary Angles,
because they add up to 180°.
Notice that together they make a
straight angle.
But the angles don't have to be
together.
These two are supplementary
because 60° + 120° = 180°
If the two angles add to 180°, we say they
"Supplement" each other.
Supplement comes from Latin supplere, to
complete or "supply" what is needed.
Spelling: be careful, it is not
"Supplimentary Angle" (with an "i")
Complementary vs Supplementary
A related idea is Complementary Angles, they add up to 90°
How can you remember which is which? Easy! Think:


"C" of Complementary stands for "Corner"
(a Right Angle), and
"S" of Supplementary stands for "Straight" (180 degrees is a straight line)
You could also think "Supplement" (like a Vitamin Supplement) is something extra, so it it
bigger.
Vertical Angles
Vertical Angles are the angles opposite each other when two lines cross
"Vertical" in this case means they share the same Vertex (corner point), not the usual meaning
of up-down.
In this example, a° and b° are vertical angles.
The interesting thing here is that vertical angles are equal:
a° = b°
(in fact they are congruent angles)
Example: Find angles a°, b° and c° below:
Because b° is vertically opposite 40°, it must also be 40°
A full circle is 360°, so that leaves 360° − 2×40° = 280°
Angles a° and c° are also vertical angles, so must be equal, which means they are 140° each.
Answer: a = 140°, b = 40° and c = 140°.