GEOMETRY (HOLT 1 -4) K.SANTOS

Pairs of Angles

Adjacent Angles

Adjacent angles—two angles in the same plane (coplanar) with a common vertex, a common side but no common interior points

A D

B C

< ABD and <DBC are adjacent angles

Linear Pair

Linear Pair—a pair of adjacent angles whose noncommon sides are opposite sides

1 2

< 1 and < 2 form a linear pair

Complementary Angles

Complementary Angles—two angles whose measures have a sum of 90

A D

30 60 B C

Adjacent and non-adjacent andComplementary complementary<ABD and <DBC 30= 90

Example---Complementary angles

Given: m< 1 =3x + 7 and m < 2= 7x + 3. Find x, m< 1 and m < 2. The angles are complementary.The angles are complementary(So they add to 90 m< 1 + m < 2 = 903x + 7 + 7x + 3 = 90

10x + 10 = 90 1 210x = 80

x= 8

m<1= 3x + 7 m < 2 =7x + 3m<1= 3(8) + 7 m< 2 = 7(8) + 3m< 1 = 31 m < 2 =59 check: 31 + 59 = 90 which are complementary

Supplementary Angles

Supplementary Angles—two angles whose measures have the sum is 180

1 2 110 70

Adjacent and Non-adjacent andSupplementary supplementary

m<1 + m < 2 = 180 110 = 180

Example—Supplementary Angles

Given m< 2 = 125Find the m< 1:

This is a linear pairSo the angles are supplementary(which means they add to 180 2

1m< 1 + m< 2 = 180x + 125 = 180x = 55So m<1 = 55

Complements and Supplements

If you have an angle X

It’s complement can be found by subtracting from 90 or (90 – x)

It’s supplement can be found by subtracting from 180 or (180 - x)

Example—Supplements and Complements

Given: m <A = 72 and m <B = (4x – 12)

1. Find the complement and supplement of <A. Complement: 90 – 72 = 18 (or 72 + x = 90)

Supplement: 180 – 72 = 108 (or 72 + x = 180)

2. Find the complement and supplement of <B.Complement: 90– (4x -12)

90 – 4x + 12 (102 – 4x)

Supplement: 180 – (4x -12) 180 – 4x + 12 (192 – 4x)

VerticalAngles

Vertical angles—two angles whose sides form two pairs of opposite rays

1 3

2 4 Picture always looks like an X

< 1 and < 4 are vertical angles< 2 and < 3 are vertical angles

Example—Identifying angle pairs

Name a pair of each of the following angles: E F

Complementary angles: D <ADB and <BDC

A B CSupplementary angles: <ADE and <EDF

Vertical angles: <EDA and <FDC