Download 1.5 Exploring Angle Pairs

1.5 Exploring Angle Pairs
SOL: G4
Objectives: The Student Will …
• Identify and use special pairs of angles.
• Use special angle pairs to determine angle measure.
Adjacent Angles
Two coplanar angles
 Have a common vertex
 Have a common side, but no common
interior points.

Examples:
∡ABC and ∡CBD
Nonexamples:
∡ABC and ∡ABD
∡ABC and ∡BCD
C
A
D
A
C
C
C
D
D
B
A
B
D
B
A
B
Are they Adjacent or Not???
A
N
O
B
J
Y
Z
D
X
C
K
ADB, BDC
M
OKN, MJL
W
V
WVX, XVZ
L
Vertical Angles

Are two nonadjacent angles
Formed by two intersecting lines

Think of a bow tie

For every set of intersecting lines there are two
sets of congruent angles

Examples: ∡AEB and ∡CED, ∡AED and ∡BEC
A
B
D
E
C
Are they Vertical or Not???
G
X
W
H
E
I
F
V
J
Y
EFG, GFH
Z
YVZ, WVX
IHJ, EHJ
YVZ, ZVW
XVY, WVZ
ZVW, WVX
Complementary Angles

Two angles whose measures have a sum of 90

Examples:
1 and 2 are complementary
PQR and XYZ are complementary
P
50°
1
2
R
Q
X
Y
40°
Z
Example of Complimentary Angles
53
15
60
?
37
75
Supplementary Angles

Two angles whose measures have a sum of 180

Example:
EFH and HFG are supplementary
M and N are supplementary
H
M
E
F
G
80°
N
100°
Examples of Supplementary
Angles
130
45
50
135
Linear Pair



Is a pair of adjacent angles
Whose noncommon sides are opposite rays
The angles of a linear pair forms a straight line
Example: ∡BED and ∡BEC
B
C
E
D
Are they a Linear Pair or Not???
G
Z
H
E
I
F
J
EFG, GFH
W
Y
YXZ, WXZ
IHJ, EHJ
EFG, IHJ
X
YXW, WXZ
Example 1:
Refer to the figure below. Name an angle pair that
satisfies each condition.
a.) two angles that form
a linear pair.
b.) two acute vertical angles.
Example 2:
∡KPL and ∡JPL are a linear
pair, m∡KPL = 2x + 24, m∡4x + 36. What are
the measures of ∡KPL and ∡JPL?
Since ∡KPL and ∡JPL are a linear pair,
then we know their sum is 180°
(2x + 24)° (4x + 36)°
m∡KPL + m∡JPL = 180°
(2x + 24) + (4x + 36) = 180°
6x + 60 = 180°
- 60 - 60
6x = 120°
6x = 120°
6
6
x = 20°
m∡KPL = 2(20) + 24 =
64°
m∡JPL = 4(20) + 36 =
116°
Angle Bisector

A ray that divides an angle into two
congruent angles

Example: If PQ is the angle bisector of
RPS, then RPQ  QPS
R
Q
S
P
Examples 3:
W
A
B
Angle Bisector
D
X
Z
Y
C
If mADB = 35,
35
then mBDC = ___
70
then mADC = ___
If mYZX = 20,
then mWZX = ___
20
then mWZY = ___
40
Example 4:
If BX bisects ABC, find x and mABX
and mCBX. Bisector cuts and angle into two equal
parts. Then m∡ABX = m∡CBX
A 3x + 5
B
m∡ABX =
3xm∡CBX
+ 5 = 2x + 30
X
2x + 30
C
-2x
-2x
x + 5 = 30
- 5 -5
x = 25
m∡ABX = 3(25) + 5 = 80°
m∡CBX = 2(25) + 30 = 80°