Geometry Section 1.6

Special Angle Pairs

Two angles are adjacent angles if

Two angles are vertical angles if

common.in side a share and vertex same thehavethey

intersect. lines two

when formed angles opposite thearethey

...or 3 and 2or 2 and 1

4 and 2or 3 and 1

While a postulate is

a theorem is a

proof without trueas acceptedstatement a

proven. becan that statement a

Theorem 2.6: Vertical Angle Theorem:

congruent. arethen they

angles, verticalare angles twoIf

Complementary angles are two angles whose measures have a

sum of 90 degrees.

Each angle is called a __________ of the other.

complement

Supplementary angles are two angles whose measures have a

sum of 180 degrees.

Each angle is called a ___________ of the other.

supplement

Example 1: Complete the chart.

27 11745 45

)90( x )180( x

18018573 xx

375.19

1558

180258

x

x

x

875.114

125.65

Bm

Am

Example 3: The measure of an angle is 10 less than three times the measure of its complement. Find the measure of both angles.

supplement x-180

compliment90

angle

x

x x 10)90(3 x

65

2604

103270

x

x

xx

25 & 65

A linear pair is two angles which share a side in common and whose noncommon sides form a straight

line.

Linear Pair Postulate

If two angles form a linear pair, then they are supplementary.

Example 4: Name all angles that form a linear pair with .BMA

AME

BMD

63 x

52 x

y5

2.36

1815

18015

1805263

x

x

x

xx

4.775)2.36(2 48.15

4.775

y

y