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Pairs of Angles

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Pairs of Angles

Geometry (Holt 1-4)k.Santos

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

1 2

< 1 and < 2 form a linear pair

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

A D

30 60

B C

Adjacent and non-adjacent and

Complementary complementary

<ABD and <DBC30= 90

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 = 90

3x + 7 + 7x + 3 = 90

10x + 10 = 90 1 2

10x = 80

x= 8

m<1= 3x + 7 m < 2 =7x + 3

m<1= 3(8) + 7 m< 2 = 7(8) + 3

m< 1 = 31 m < 2 =59

check: 31 + 59 = 90 which are complementary

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

1 2 110 70

Adjacent and Non-adjacent and

Supplementarysupplementary

m<1 + m < 2 = 180110 = 180

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

This is a linear pair

So the angles are supplementary

(which means they add to 1802

1

m< 1 + m< 2 = 180

x + 125 = 180

x = 55

So m<1 = 55

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)

Given: m <A = 72and m <B = (4x – 12)

Find the complement and supplement of <A.

Complement: 90 – 72 = 18 (or 72 + x = 90)

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

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)

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

13

24

Picture always looks like an X

< 1 and < 4 are vertical angles

< 2 and < 3 are vertical angles

Name a pair of each of the

following angles: E F

Complementary angles: D

<ADB and <BDC

A B C

Supplementary angles:

<ADE and <EDF

Vertical angles:

<EDA and <FDC