Adjacent, Vertical, Supplementary, and Complementary Angles.
GEOMETRY (HOLT 1-4)K.SANTOS Pairs of Angles. Adjacent Angles Adjacent angles—two angles in the...
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Transcript of GEOMETRY (HOLT 1-4)K.SANTOS Pairs of Angles. Adjacent Angles Adjacent angles—two angles in the...
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