Download Section 1.5 - Angle Pairs

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Simplify each expression.
1. 90 – (x + 20)
70 – x
2. 180 – (3x – 10)
190 – 3x
Correcting Assignment #3
Evens only in this section (6-22 even)
Correcting Assignment #3
Evens only in
this section
(6-22 even)
Correcting Assignment #3
Selected Problems in this section
(22, 24-27, 29, 30)
Chapter 1-5 Exploring Angle Pairs
Target
Identify special angle pairs and use their
relationships and find angle measures.
Vocabulary
adjacent angles
linear pair
vertical angles
complementary angles
supplementary angles
angle bisector
Vertical Angles
Vertical angles are two nonadjacent angles formed
by two intersecting lines. 1 and 3 are vertical
angles, as are 2 and 4. Vertical angles are
congruent.
An angle bisector is a ray that divides an angle
into two congruent angles.
JK bisects LJM; thus LJK  KJM.
Example 1: Identifying Angle Pairs
Adjacent, non-adjacent, vertical? Which is it?
AEB and CED
AEB and CED are
non-adjacent
AEB and BED
AEB and BED are
adjacent
Example 1: Identifying Angle Pairs
What else do we know about AEB and BED?
AEB and BED are adjacent angles that form a
linear pair because they combine to create a straight
angle. Linear pairs are also supplementary because
they add to 180⁰.
Example 2: Identifying Angle Pairs
What can we say about 3
and 5 which are formed
by the intersection of lines
l and m?
3 and 5 are vertical angles, meaning they
have the same measurement.
And what about 1 and 2?
l
m
Example 2: Identifying Angle Pairs
l
m
1 and 2 are adjacent angles
1 and 2 are also congruent
The ray between them is called an angle bisector
If m4 = 28⁰, what is m2?
m2 = 14⁰
Example 3: Finding the Measures of
Complements and Supplements
Find the measure of each of the following.
A. complement of F
(90 – mF)
90 – 59 = 31
B. supplement of G
(180 – mG)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Example 4: Finding the Measure of an Angle
KM bisects JKL
mJKM = (4x + 6)°
mMKL = (7x – 12)°
Find mJKM.
Begin by setting the angles equal to one another.
mJKM = mMKL
Therefore,
4x + 6 = 7x - 12
Example 4 Continued
Step 1 Find x.
mJKM = mMKL
Def. of  bisector
(4x + 6)° = (7x – 12)°
+12
+12
Substitute the given values.
Add 12 to both sides.
4x + 18
–4x
= 7x
–4x
18 = 3x
6=x
Simplify.
Subtract 4x from both sides.
Divide both sides by 3.
Simplify.
Example 4 Continued
Step 2 Find mJKM.
mJKM = 4x + 6
= 4(6) + 6
Substitute 6 for x.
= 30
Simplify.
Assignment #4 pg 38-39
Foundation:
7 – 21
Core:
26, 28, 29, 33-36
Challenge:
40