1. 1.4 Exploring Angle Pairs Objectives: The Student Will …
Identify and use special pairs of angles.
Use special angle pairs to determine angle measure.

2. 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 A C D B A B D C A C D B A B C D

3. Are they Adjacent or Not???L M N O K J A B C D W X Y Z V
ADB, BDC
OKN, MJL
WVX, XVZ

4. 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 C E D

5. Are they Vertical or Not???F G H I J W X Y Z V
EFG, GFH
YVZ, WVX
IHJ, EHJ
YVZ, ZVW
XVY, WVZ
ZVW, WVX

6. Complementary Angles Two angles whose measures have a sum of 90
Examples:
1 and 2 are complementary
PQR and XYZ are complementary P R Q Y Z X
50°
40° 1 2

7. Example of Complimentary Angles
53
15
60
37 ?
75

8. Supplementary Angles Two angles whose measures have a sum of 180
Example:
EFH and HFG are supplementary
M and N are supplementary
80°
100° N M E F G H

9. Examples of Supplementary Angles
130
50
45
135

10. 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
Common
Side C B E D
Noncommon Sides
Are opposite rays
“straight line”

11. Are they a Linear Pair or Not???F G H I J Z W X
EFG, GFH Y
YXZ, WXZ
IHJ, EHJ
YXW, WXZ
EFG, IHJ

12. 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.

13. Example 2:
∡KPL and ∡JPL are a linear pair, m∡KPL = 2x + 24, m∡4x What are the measures of ∡KPL and ∡JPL?
(2x + 24)°
(4x + 36)°
Since ∡KPL and ∡JPL are a linear pair,
then we know their sum is 180°
m∡KPL + m∡JPL = 180°
(2x + 24) + (4x + 36) = 180°
6x + 60 = 180°
m∡KPL = 2(20) + 24 = 64°
6x = 120°
m∡JPL = 4(20) + 36 = 116°
6x = 120°
x = 20°

14. 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

15. Examples 3: Angle Bisector If mYZX = 20, If mADB = 35,W Z A B C D
Angle Bisector
If mYZX = 20,
If mADB = 35,
then mWZX = ___
20
35
then mBDC = ___
then mWZY = ___
40
then mADC = ___
70

16. 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
m∡ABX = m∡CBX A X C B
3x + 5
2x + 30
3x + 5 = 2x + 30
-2x x
x + 5 = 30
x = 25
m∡ABX = 3(25) + 5 = 80°
m∡CBX = 2(25) + 30 = 80°