1. Angles

2. Angle and Points ray vertex ray
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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
B is the vertex. E D
Points A, B and C are on the angle. B C
D is in the interior
E is in the exterior.

3. Naming an Angle Vertex must be the middle letter
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Naming an Angle
Using 3 points:
Vertex must be the middle letter
This angle can be named as
Using 1 point:
Using only vertex letter
Using a number: A
Use the notation m2, meaning the measure of 2. B C

4. Example K is the vertex of more than one angle.
4/19/2017
Example
Name all the angles in the diagram below
K is the vertex of more than one angle.
Therefore, there is NO in this diagram.

5. Example
Name the three angles in the diagram.

6. 4 Types of Angles Acute Angle: Right Angle: Obtuse Angle:
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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 .

7. Angle Addition Postulate Same idea as the segment addition postulate
4/19/2017
Angle Addition Postulate Same idea as the segment addition postulate
Postulate:
The sum of the two smaller angles will always equal the measure of the larger angle.
Complete:
m  ____ + m  ____ = m  _____
MRK
KRW
MRW

8. Example Fill in the blanks.
m < ______ + m < ______ = m < _______

9. 4/19/2017
Adding Angles
If you add m1 + m2, what is your result?
m1 + m2 = 58.
Also…
m1 + m2 = mADC
Therefore, mADC = 58.

10. Example First, draw it! mMRK = 3x = 3•21 = 63º
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Example
K is interior to MRW, m  MRK = (3x), m KRW = (x + 6) and mMRW = 90º. Find mMRK.
First, draw it!
3x + x + 6 = 90
4x + 6 = 90
– 6 = –6
4x = 84
x = 21 3x
x+6
Are we done?
mMRK = 3x = 3•21 = 63º

11. Example
Given that m< LKN = 145, find m < LKM and m < MKN

12. Example
Given that < KLM is a straight angle, find m < KLN and m < NLM

13. Example
Given m < EFG is a right angle, find m < EFH and m < HFG

14. 4/19/2017
Angle Bisector
An angle bisector is a ray in the interior of an angle that splits the angle into two congruent angles. 5 3

15. 3   5. Congruent Angles Definition:
4/19/2017
Congruent Angles
Definition:
If two angles have the same measure, then they are congruent.
Congruent angles are marked with the same number of “arcs”. 3 5
3   5.

16. Example: is an angle bisector J T
Which two angles are congruent?
<JUK and < KUT or < 4 and < 6

17. Example:
Given bisects < XYZ and m < XYW = Find m < XYZ

18. Example:
Given bisects < ABC. Find m < ABC