ANGLES
Naming An Angle
To name an angle, we name any point on one ray, then the
vertex, and then any point on the other ray.
A
B
C
For example: ABC or CBA
We may also name this angle only by the single letter of the
vertex, for example B.
Types Of Angles
There are four main types of angles.
Right angle
90o
Acute angle
Less than 90o
A
B
Obtuse angle
More than 90o
A
A
C
B
B
C
Straight angle
180o
A
B
C
C
Which of the angles below is a right angle, acute angle and
an acute angle?
1.
2.
D
E
P
R
Q
F
Obtuse angle
3.
Right angle
B
A
C
Acute angle
Congruent Angles
Two angles that have the same measure are called congruent
angles.
D
A
B
300
C
E
300
F
Congruent angles have the same size and shape.
Adjacent Angles
Two angles that have a common vertex and a common ray
are called adjacent angles.
A
D
Common ray
B
Common vertex
C
Adjacent Angles ABD and DBC
Adjacent angles do not overlap each other.
Vertically Opposite Angles
Vertically opposite angles are pairs of angles formed by two
lines intersecting at a point.
C
A
P
B
D
APC = BPD
APB = CPD
Vertically opposite angles are congruent.
Complimentary Angles
If the sum of two angles is 900, then they are called
complimentary angles.
A
D
600
B
E
C
300
F
ABC and DEF are complimentary because
ABC + DEF
600 + 300 = 900
Supplementary Angles
If the sum of two angles is 1800 then they are called
supplementary angles.
A
P
1000
Q
800
R
B
C
PQR and ABC are supplementary, because
PQR + ABC
1000 + 800 = 1800
Pairs Of Angles Formed by a Transversal
A line that intersects two or more lines at different points is
called a transversal.
(transversal)
G
A
C
P
B
Q
D
F
Eight angles are formed in all by the transversal.
Corresponding Angles
A transversal creates pairs of corresponding angles. (angles
in the same spot in both lines)
L
Line L
GPB = PQE
G
A
D
P
B
Q
E
F
Line M
Line N
GPA = PQD
BPQ = EQF
APQ = DQF
Four pairs of corresponding angles are formed.
Corresponding pairs of angles are congruent.
Alternate Interior Angles
Alternate interior angles are formed on opposite sides of the
transversal on the inside of the lines.
L
G
A
D
Line L
P
B
Q
E
Line M
Line N
BPQ = DQP
APQ = EQP
F
Pairs of alternate interior angles are congruent.
Alternate Exterior Angles
Alternate exterior angles are formed on opposite sides of the
transversal and on the outside of the lines.
L
G
A
P
B
BPG = DQF
APG = EQF
D
Q
E
F
Pairs of alternate exterior angles are congruent.
Same Side Interior Angles
The angles that lie in the area between the two parallel lines
that are cut by a transversal, are called same side interior
angles.
L Line L
G
0

BPQ
+

EQP
=
180
Line M
0
P
60
A 1200
B
1200
600
D
E
Q
Line N
APQ + DQP = 1800
F
interior
eachside
pairofadd
AThe
pairmeasures
of interiorofangles
lieangles
on the in
same
theup to 1800.
transversal.
Same Side Exterior Angles
The angles that lie in the area outside the two parallel lines
that are cut by a transversal, are called same side exterior
angles.
L Line L
G
1200
600
0

BPG
+

EQF
=
180
Line M
P
A
B
D
600E
Q
1200
Line N
APG + DQF = 1800
F
The measures of exterior angles in each pair add up to
1800.
Angles in a Triangle

All angles in a triangle will add up to 180o
= 80o
= 60o
Name the pairs of the following angles formed by a
transversal.
Line
Line LL
GG
Line L
G
A A
P
A
500
P
P
B
B
B
1300
D D
D
QQ
Q
FF
F
EE
E
LineMM
Line
Line M
LineNN
Line
Line N