Download 1.6 Angle Pair Relationships

1.6 Angle Pair Relationships
What you should learn
GOAL
1
Identify vertical angles and linear pairs.
GOAL
2
Identify complementary and supplementary
angles.
Why you should learn it
To solve real-life problems, such as finding the
measures of angles formed by the cables of a bridge.
1.6 Angle Pair Relationships
GOAL
1
VERTICAL ANGLES AND LINEAR PAIRS
Vocabulary
Two angles whose sides form two pairs of opposite rays
vertical angles
are called _____________.
4
1
3 2
Identify the pairs of vertical
angles in the diagram.
Click to check.
1 and 3
2 and 4
Two adjacent angles whose noncommon sides are
opposite rays are called a _________.
linear pair
common side
5
6
noncommon sides
5 and 6 are a linear pair.
EXAMPLE 1
Extra Example 1
2
1
3
5 4
a. Are 1 and 2 a linear pair?
yes
b. Are 4 and 5 a linear pair?
no
c. Are 5 and 3 vertical angles?
no
d. Are 1 and 3 vertical angles?
yes
Click to see the answers.
EXAMPLE 2
Extra Example 2
In one town, Main Street and Columbus Avenue intersect to
form an angle of 36°. Find the measures of the other three
angles.
Click to see a diagram.
Columbus Avenue
mX  144
mY  36
36° Main Street
mZ  144
Click to see the answers.
EXAMPLE 3
Extra Example 3
Solve for x and y. Then find the angle measures.
M
Click for a hint.
L
(4 x  15)
P (5 x  30)
N
(3 y  15)
(3 y  15)
mLPM  mNPM  180
and mLPO  mNPO  180
Solve each equation to find x
and y. Click for the answers.
x  15, y  30
O
mLPM  mOPN  75
mMPN  mLPO  105
Checkpoint
1. Name one pair of vertical angles and one pair of angles
that form a linear pair. Click to see the answers.
J
I
(5 x  30)
K
(2 x  4)
H
G
Vertical angle pairs: IHJ and GHK ; JHK and GHI
Linear pairs: IHJ and JHK ; JHK and KHG;
KHG and GHI ; GHI and IHJ
2. What is the measure of GHI ? 140
1.6 Angle Pair Relationships
GOAL
2
COMPLEMENTARY AND SUPPLEMENTARY
ANGLES
Vocabulary
If the sum of the measures of two angles is 90°, the angles
are ______________
complementary angles, and each is the
___________ of the other.
complement
1 and 2 are now
nonadjacent
complementary angles.
Note: Complementary angles
1
may or may not be adjacent.
2
If the sum of the measures of two angles is 180°, the
supplementary angles, and each is the
angles are _____________
___________
supplement of the other.
Note: Supplementary angles may or may not be adjacent.
If 3 and 4 are adjacent and supplementary, they form a
_________.
linear pair
3
4
3 and 4 are now nonadjacent supplementary angles,
and they no longer form a linear pair.
EXAMPLE 4
Extra Example 4
State whether the two angles are complementary,
supplementary, or neither. Click for the solution.
12
9
3
6
neither
supplementary
12
9
3
neither
6
EXAMPLE 5
Extra Example 5
a. Given that G is a supplement of H , and mG is 82,
find mH .
mG  mH  180
Click to see
82  mH  180
the solution.
mH  98
b. Given that U is a complement of V , and mU is 73,
find mV .
mU  mV  90
Click to see
73  mV  90
the solution.
mV  17
EXAMPLE 6
Extra Example 6
T and S are supplementary. The measure of T is half
Find
S.
mSClick
.
the measure of
for a hint.
1
mT  mS  180 and mT  mS
2
Substitute and solve. Click for the solution.
mT  mS  180
1
mS  mS  180
2
3
mS  180
2
mS  120
Checkpoint
D and E are complements and D and F are
supplements. If mE is four times mD, find the
measure of each of the three angles. Click for a hint.
mE  4(mD) and mE  mD  90
Substitute and solve. Click for the answers.
mD  18
mE  72
mF  162
QUESTIONS?