1.6 Angle Pair Relationships

Which angles are adjacent?

1 32

4

<1&<2, <2&<3, <3&<4, <4&<1

Vertical Angles – 2 angles that share a common vertex & whose sides form 2 pairs of opposite rays.

<1&<3, <2&<4

Then what do we call <1&<3?

Linear Pair (of angles)

• 2 adjacent angles whose non-common sides are opposite rays.

1 2

Example• Vertical angles?

<1 & <4• Adjacent angles?

<1&<2, <2&<3, <3&<4, <4&<5, <5&<1• Linear pair?

<5&<4, <1&<5• Adjacent angles not a linear pair?

<1&<2, <2&<3, <3&<4

1 3

2

5 4

Important Facts

• Vertical Angles are congruent.

• The sum of the measures of the angles in a linear pair is 180o.

Example:

• If m<5=130o, findm<3m<6m<4

5 3

4

6

=130o

=50o

=50o

Example:• Find x

ym<ABEm<ABDm<DBCm<EBC

3x+5o y+20ox+15o 4y-15o

x=40

y=35

m<ABE=125o

m<ABD=55o

m<DBC=125o

m<EBC=55o

A

B

C

D

E

Complementary Angles

• 2 angles whose sum is 90o

1

2

35o

A

55o

B<1 & <2 are complementary

<A & <B are complementary

Supplementary Angles• 2 angles whose sum is 180o

1 2

130o 50o

X Y

<1 & <2 are supplementary.

<X & <Y are supplementary.

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