Download ABD and <DBC are adjacent angles

Pairs of Angles
GEOMETRY (HOLT 1-4)
K.SANTOS
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°
B
60°
C
Adjacent and
Complementary
<ABD and <DBC
non-adjacent and
complementary
30° + 60°= 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 = 90°
3x + 7 + 7x + 3 = 90
10x + 10 = 90
10x = 80
x= 8
1 2
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
 Supplementary Angles—two angles whose
measures have the sum is 180°
1
2
110°
70°
Adjacent and
Supplementary
Non-adjacent and
supplementary
m<1 + m < 2 = 180°
110° + 𝟕𝟎° = 180°
Example—Supplementary Angles
 Given m< 2 = 125°. Find the m< 1:
This is a linear pair
So the angles are supplementary
(which means they add to 180°)
m< 1 + m< 2 = 180°
x + 125 = 180
x = 55
So m<1 = 55°
2
1
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
2
3
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
Complementary angles:
<ADB and <BDC
D
A
Supplementary angles:
<ADE and <EDF
Vertical angles:
<EDA and <FDC
F
B
C