Download 1.6 Angle Pair Relationships

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Transcript 
1.6 Angle Pair Relationships
Adjacent Angles
 Remember:
Adjacent Angles
share a vertex and
a ray, but DO NOT
share any interior
points.
Which angle pairs are adjacent?
<1&<2 <2&<3 <3&<4 <4&<1
Then what do we call <1&<3?
2
1
3
4
Vertical Angles – 2 angles
that share a common vertex &
whose sides form 2 pairs of
opposite rays. Vertical Angles
are always congruent!
<1&<3, <2&<4
Linear Pair (of angles)
2
adjacent angles whose non-common
sides are opposite rays.
Basically, it’s 2 adjacent angles that together make
a straight line!
Example
 Vertical
angles?
<1 & <4
 Adjacent angles?
<1&<2, <2&<3,
<3&<4, <4&<5, <5&<1
 Linear pair?
<5&<4, <1&<5
 Adjacent angles not a linear pair?
<1&<2, <2&<3, <3&<4
2
1
5
3
4
Important Facts
 Vertical
Angles are congruent. ALWAYS! THIS IS ONE
ASSUMPTION YOU CAN ALWAYS MAKE!
 The
sum of the measures of the angles in a linear
pair is 180o. REMEMBER: THE TWO ANGLES IN A
LINEAR PAIR ARE Adjacent ANGLES THAT MAKE A
STRAIGHT LINE!
Example:
m<5=130o, find
o
=
130
m<3
m<6 =50o
m<4 =50o
4
 If
5
3
6
Example:
x and y and
m<ABE
m<ABD
m<DBC
m<EBC
A
E
 Find
B
D
C
m<CBE + m<EBA = 180° Linear Pair
x + 15 + 3x + 5 = 180
Substitute
4x + 20 = 180
CLT
4x = 160
Subtraction
x = 40
Division
m<CBD + m<ABD = 180
4y -15 + y + 20 = 180
5y + 5 = 180
5y = 175
y = 35
Linear Pair
Substitute
CLT
Subtraction POE
Division POE
x=40
y=35
m<ABE=125o
m<ABD=55o
m<DBC=125o
m<EBC=55o
Complementary Angles
2
angles whose sum is 90o.
 The two angles DO NOT need to be
adjacent!
35o
1
2
<1 & <2 are complementary
<A & <B are complementary
55o
A
B
Supplementary Angles
2
angles whose sum is 180o.
 Two angles can be supplementary and
NOT BE A LINEAR PAIR.
<1 & <2 are
supplementary.
<X & <Y are
supplementary.
130o
X
50o
Y
Ex: <A & <B are supplementary. m<A is 5
times m<B. Find m<A & m<B.

Let’s say
m<A = 5b
m<B = b
Angle A’s measure is 3 times its complement,
<B. The measure of angle A’s supplement, <C,
is 5 times m<B. Find the measures of all the
angles.
 m<A
+ m<B = 90°
3b + b = 90

4b = 90
b = 22.5
 m<A
= 3*22.5=
67.5°
 m<C = 5b, so
5(22.5) = 112.5°
 Let’s
say:
 m<B = b
 m<A = 3b
 m<C = 5b
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