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Introduction to Angles
Definitions
Vertex: Common endpoint of the two rays that make
an angle.
A
Point B is the vertex of ∠𝑨𝑩𝑪
B
C
Sides: The two rays that make up the angle.
A
side
𝑩𝑨 and 𝑩𝑪 are sometimes
B
called sides.
side
C
Angle and Points

An Angle is a figure formed by two rays with a common endpoint,
called the vertex.
ray
vertex

ray
Angles can have points in the interior, in the exterior or on the
angle.
A
E
D
B
C
Points A, B and C are on the angle. D is in the interior and E is in the exterior.
B is the vertex.
Lesson 1-4: Angles
3
Naming an angle: (1) Using 3 points
(2) Using 1 point
(3) Using a number – next slide
Using 3 points: vertex must be the middle letter
This angle can be named as ABC or CBA
Using 1 point: using only vertex letter
* Use this method is permitted when the vertex point is the vertex
of one and only one angle.
Since B is the vertex of only this angle, this can
also be called B .
B
Lesson 1-4: Angles
A
C
4
Naming an Angle - continued
Using a number: A number (without a degree symbol) may be
used as the label or name of the angle. This
A
number is placed in the interior of the angle near
its vertex. The angle to the left can be named
B
2
C
as 2 .
* The “1 letter” name is unacceptable when …
more than one angle has the same vertex point. In this case, use
the three letter name or a number if it is present.
Lesson 1-4: Angles
5
Definitions
Measure of an angle: Smallest amount of rotation
about the vertex from one ray to the other. Use a
curved line to indicate the angle.
A
B
𝟐𝟒°
C
Degrees: The unit of measure for angles. Indicates the
amount of rotation.
∠𝑨𝑩𝑪 = 𝟐𝟒°
Example

K is the vertex of more than one angle.
Therefore, there is NO K in this diagram.
There is LKM , PKM , and LKP
There is also 2 and 3 but there is no 5!!!
L
M
2
K
3
Lesson 1-4: Angles
P
7
4 Types of Angles
Acute Angle: an angle whose measure is less than 90.
Right Angle: an angle whose measure is exactly 90 .
Obtuse Angle: an angle whose measure is between
90 and 180.
Straight Angle: an angle that is exactly 180 .
Lesson 1-4: Angles
8
Definitions
Congruent Angles: Angles that have the same degree
measure. Used a curved line above an equal sign to
indicate congruence.
A
X
≅
B
C
Y
Z
∠𝑨𝑩𝑪 ≅ ∠𝑿𝒀𝒁
Said: “Angle ABC is congruent to angle XYZ.”
Practice
Name all the angles in this figure. P
∠𝑷𝑿𝑮
∠𝑮𝑿𝑴
∠𝑷𝑿𝑴
∠𝑿𝑴𝑮
∠𝑿𝑮𝑨
∠𝑿𝑮𝑴
∠𝑴𝑮𝑨
X
M
G
A
Measuring, calculating and
drawing angles...
0011 0010 1010 1101 0001 0100 1011
1
2
4
0011 0010 1010 1101 0001 0100 1011
A protractor
1
2
4
Here is a standard protractor like you
use in the classroom.
When we use a protractor, we
need to line it up correctly.
0011 0010 1010 1101 0001 0100 1011
1
2
4
You need to make sure the protractor is lined up correctly.
Is this ready to measure the angle?
Were you right......................it wasn’t
0011 0010 1010 1101 0001 0100 1011
1
2
4
Look for the upside down ‘T’ in the middle of
the straight line on your protractor.
This needs to be exactly on the vertex of
your angle.
We need to remember.....
0011 0010 1010 1101 0001 0100 1011
It doesn’t
matter which
way round the
angle is, you
ALWAYS need
to line the upside
down ‘T’ to the vertex
of the angle.
1
2
4
Now you are ready.
0011 0010 1010 1101 0001 0100 1011
1
2
4
Read from the 0°, and follow the inner set of
numbers.
Once you reach 30° you need to be
careful!!!
0011 0010 1010 1101 0001 0100 1011
1
2
4
You then need to look at the 1° markings on
the outer set of numbers.
What does it measure?
0011 0010 1010 1101 0001 0100 1011
1
This angle measures 35°.
2
4