1. Lesson 1-4
Angles

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Definition of an angle
An Angle is a figure formed by two rays with a common endpoint, called the vertex
ray
vertex
ray

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Angles and Points
Angles can have points in the interior, in the exterior or on the angle.
Points A, B and C are on the angle, D is in the interior and E is in the exterior.
B is the vertex.

4. Naming an angle An angle can be named several different ways.
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Naming an angle
An angle can be named several different ways.
You can always use three points.
You can use one point sometimes.
You can use a number sometimes.

5. Using three points One name for this angle is <ABC
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Using three points
One name for this angle is <ABC
The vertex point MUST be the middle letter
You can also name this angle <CBA

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Using one letter
Sometimes angles can be named by their vertex letter only
You can only use this method if the vertex point is the vertex of ONLY ONE angle
Since B is the vertex of only this angle, this can also be called <B

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Using a number
Sometimes there is a number written inside the angle close to the vertex
This is the name of the angle, not its measurement
This angle can also be called <2

8. When you cannot use one letter to name an angle
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When you cannot use one letter to name an angle
If more than one angle has the same vertex point, then you cannot use just the vertex to name the angle
In this case, use the three letter name or a number if it is present
See this example:

9. Example K is the vertex of more than one angle.
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Example
K is the vertex of more than one angle.
Therefore, there is NOT an <K in this diagram.
There is <LKM, <PKM and <LKP
There is also <2 and <3 BUT THERE IS NOT AN <5!!

10. Types of Angles There are four different types of angles:
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Types of Angles
There are four different types of angles:
Acute angle: an angle whose measure is less than 90.
Right angle: an angle whose measure is exactly 90 .

11. Types of Angles between 90 and 180. exactly 180 .
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Types of Angles
Obtuse angle: an angle that is
between 90 and 180.
Straight angle: an angle that is
exactly 180 .

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Adding Angles
When you want to add angles, use the notation m<1, meaning the measure of <1.
If you add m<1 + m<2, what is your result?
m<1 + m<2 = 58.
m<1 + m<2 = m<ADC also.
Therefore, m<ADC = 58.

13. Angle Addition Postulate
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Angle Addition Postulate
That last example is an example of the Angle Addition Postulate.
This postulate states that the sum of the two smaller angles will always equal the measure of the larger angle.
Complete:
m< ____ + m< ____ = m< _____
MRK
KRW
MRW

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Angle Bisector
What if a ray in the interior of an angle splits the angle into two congruent angles?
This ray would be called
an Angle Bisector.
Since <4  <6,
then is an
angle bisector.

15. Example Draw your own diagram and answer this question:
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Example
Draw your own diagram and answer this question:
If is an angle bisector of <PMY and m<PML = 87, then find:
m<PMY = _______
m<LMY = _______