1. 1.6 Angle Pair Relationships
p.44

2. Which angles are adjacent?
<1&<2, <2&<3, <3&<4, <4&<1
Then what do we call <1&<3?
2 Vertical Angles – 2 angles
1 3 that share a common vertex &
4 whose sides form 2 pairs of
opposite rays.
<1&<3, <2&<4

3. Linear Pair (of angles)
• 2 adjacent angles whose non-common
sides are opposite rays.
1
2

4. Example
• Vertical angles?
<1 & <4
• Adjacent angles?
2
<1&<2, <2&<3, 1 3
<3&<4, <4&<5, <5&<1 5 4
• Linear pair?
<5&<4, <1&<5
• Adjacent angles not a linear pair?
<1&<2, <2&<3, <3&<4

5. Important Facts
• Vertical Angles are congruent.
• The sum of the measures of the angles in
a linear pair is 180o.

6. Example:
• If m<5=130o, find
4
m<3 =130o
m<6 =50o 5 3
m<4 =50o
6

7. Example:
A
E
3x+5 o
• Find x B y+20 o
x+15 o
4y-15 o
y D
m<ABE C
x=40
m<ABD
y=35
m<DBC
m<ABE=125o
m<EBC
m<ABD=55o
m<DBC=125o
m<EBC=55o

8. Complementary Angles
• 2 angles whose sum is 90o
35o
1
2
55o
A
<1 & <2 are complementary B
<A & <B are complementary

9. Supplementary Angles
• 2 angles whose sum is 180o
<1 & <2 are
supplementary.
<X & <Y are
2
supplementary.
1
130o 50o
X Y

10. Ex: <A & <B are supplementary. m<A is
5 times m<B. Find m<A & m<B.
m<A + m<B = 180o
m<A = 5(m<B)
Now substitute!
5(m<B) + m<B = 180o
6(m<B)=180o
m<B=30o
m<A=150o

11. Assignment