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Lesson 4
Angles and Angle Bisector
• An angle is a figure formed by two rays with the same endpoint.
The two rays are called the sides of the angle. The endpoint is called
the vertex of the angle.
Symbol for an angle is “”
Vertex: B
Sides: BA and BC
A
We use 3 letters when naming an
angle. The vertex must be in the
middle.
The name of the angle to the left
is
B
ABC
C
CBA
B
• Two angles are congruent angles if they have the same measures.
Ex. 1
Name ALL the angles in the figure below.
Would it be correct to name any
of the angles Q? Explain.
NO, because 3 of the angles have Q
for a vertex.
You need more information in the
name to distinguish them from one
another.
It is always best to use 3 LETTERS
to name an angle
Angles are measured in units called degrees.
To indicate the degree measure of an angle,
write a lowercase m in front of the angle
symbol.
The degree measure of angle A is 80o.
mA = 80o
A protractor is used to find the measure of an angle.
1. Place the center of the
protractor over the vertex.
2. Align the protractor with
one side of the angle.
3. The second side of the angle
crosses the protractor at
So, mBAC =
65o
o
o
Measure is between 0o and 90o Measure is between 90 and 180
When you see the small
box, you know that the
measure of the angle is
90.
Measure is 90o
Measure is 180o
Angle Addition Theorem
If you add two angles together, then
they will share the vertex and the sum
will create a larger angle.
Ex 2. Find the measure PTM
PTN + NTM = PTM
Angle Add Theorem
37° + 43° =PTM
PTM = 80°
P
N
37°
43°
T
M
Ex 2. If ATD = x+21, Find the measure
ATD
ATN + NTD = ATD
x+8 +
x=1
x+12
=x+21
ATD = x+21
= (1)+21
= 22
Angle Add Theorem
A
N
x+8
x+12
T
D
Reminder: when you see “arcs” on 2 angles, the
angles are congruent.
110
An angle bisector is a ray (or a line segment)
that divides an angle into two congruent
angles. Its endpoint is at the vertex.
BD bisects ABC
A
ABD  DBC
D
B
C
Ex. 1 BD bisects ABC, and mABC = 110.
Find mABD and mDBC.
D
A
110
B
C
mABD = mDBC Def of angle bisector
= m ABC
2
= 110
2
= 55o
MP bisects LMN and mLMP = 46
Ex. 2
L
P
46
M
mLMP = mPMN
= 46o
N
a) Find mPMN and
mLMN
Def of angle bisector
LMP +PMN = LMN Angle add thr
mLMN = 2(46) = 92o
b) Determine if LMN is acute, right, obtuse or straight.
Obtuse 
Ex. 3 BD bisects ABC, mABD = (6x + 3)o,
and mDBC = (8x – 7)o. Find mABD and
mDBC. A
(6x + 3)o
D
B
(8x – 7)o
C
If an angle is
...
Acute
Right
Obtuse
Straight
then the two angles formed by
the bisector of the angle are
both...
acute
acute
acute
right
Class work
•
•
•
•
•
•
•
P 35 #1-3
P 38 #1-4, 9-10
P 37 # 4-6
P 39 # 24, 28
P 64 #2-12 (even)
P 65 #18-20
P 66 # 28,30