An angle is formed whenever two rays meet at a point.
The common point shared by the rays is called the vertex, and the rays themselves are called the sides of the angle.
Consider the following angle, made up of the rays and
There are several different ways of labeling this angle.
One way to write this angle is as follows: The symbol means "angle." Notice that the vertex is in the middle.
We can also swap the order in which we write the endpoints. For example, Notice that the vertex is still in the middle.
To save space, we sometimes write
Finally, instead of using the symbol, we can write or
Which numbered angle refers to the same angle as
If we trace along the letters of the angle name, from to to , we see that refers to the angle
Therefore, is another name for
Which numbered angle refers to the same angle as $\widehat{FGD}?$
|
a
|
$\angle{3}$ |
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b
|
$\angle{5}$ |
|
c
|
$\angle{2}$ |
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d
|
$\angle{4}$ |
|
e
|
$\angle{6}$ |
Which numbered angle refers to the same angle as $\angle{MNB}?$
|
a
|
$\angle{2}$ |
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b
|
$\angle{5}$ |
|
c
|
$\angle{1}$ |
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d
|
$\angle{3}$ |
|
e
|
$\angle{4}$ |
The measure of an angle is the amount of "turn" from one side of the angle to the other.
We measure angles in degrees, which have the symbol
Let's look at a few examples of angles with their measures.
Note the following:
The more "turn" there is, the larger the angle's measure.
A corner angle (like the angle above) has a measure of An angle with measure is called a right angle.
We use the letter to represent the measure of the angle. For example,
We'd read this as "the measure of the angle is degrees."
Which angle has a measure of
Let's highlight the angle with a measure on our diagram.
From the diagram, we see that the angle (or ) has a measure of
Which angle has a measure of $30^{\circ}?$
|
a
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$\widehat{COD}$ |
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b
|
$\widehat{BOC}$ |
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c
|
$\widehat{AOB}$ |
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d
|
$\widehat{AOD}$ |
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e
|
$\widehat{BOD}$ |
Which angle has a measure of $38^{\circ}?$
|
a
|
$\angle{COB}$ |
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b
|
$\angle{AOB}$ |
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c
|
$\angle{ODB}$ |
|
d
|
$\angle{OAB}$ |
|
e
|
$\angle{DOB}$ |
What is the measure of the angle
If we trace along the letters of the angle name, from to to we can see the angle
Therefore,
What is the measure of the angle $\widehat{CGE}?$
|
a
|
$140^\circ$ |
|
b
|
$90^\circ$ |
|
c
|
$40^\circ$ |
|
d
|
$110^\circ$ |
|
e
|
$70^\circ$ |
What is the measure of the angle $\angle{BHC}?$
|
a
|
$40^\circ$ |
|
b
|
$50^\circ$ |
|
c
|
$90^\circ$ |
|
d
|
$140^\circ$ |
|
e
|
$130^\circ$ |
