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Simplify each expression.
1. 90 – (x + 20)
2. 180 – (3x – 10)
70 – x
190 – 3x
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Correcting Assignment #3
Evens only in this section (6-22 even)
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Correcting Assignment #3
Evens only in this section (6-22 even)
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Correcting Assignment #3
Selected Problems in this section(22, 24-27, 29, 30)
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Identify special angle pairs and use their relationships and find angle measures.
Target
Chapter 1-5 Exploring Angle Pairs
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adjacent angleslinear pairvertical anglescomplementary anglessupplementary anglesangle bisector
Vocabulary
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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.
Vertical Angles
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An angle bisector is a ray that divides an angle into two congruent angles.
JK bisects LJM; thus LJK KJM.
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Adjacent, non-adjacent, vertical? Which is it?
Example 1: Identifying Angle Pairs
AEB and BED AEB and BED are adjacent
AEB and CED
AEB and CED are non-adjacent
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What else do we know about AEB and BED?
Example 1: Identifying Angle Pairs
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.
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What can we say about 3 and 5 which are formed by the intersection of lines l and m?
Example 2: Identifying Angle Pairs
l
m3 and 5 are vertical angles, meaning they have the same measurement.
And what about 1 and 2?
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Example 2: Identifying Angle Pairs
l
m
1 and 2 are adjacent angles1 and 2 are also congruentThe ray between them is called an angle bisector
If m4 = 28⁰, what is m2?m2 = 14⁰
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Find the measure of each of the following.
Example 3: Finding the Measures of Complements and Supplements
A. complement of F
B. supplement of G
90 – 59 = 31
(180 – mG)180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
(90 – mF)
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Example 4: Finding the Measure of an Angle
KM bisects JKLmJKM = (4x + 6)°mMKL = (7x – 12)°Find mJKM.
Begin by setting the angles equal to one another.
mJKM = mMKL
Therefore, 4x + 6 = 7x - 12
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Example 4 Continued
Step 1 Find x.
mJKM = mMKL
(4x + 6)° = (7x – 12)°
+12 +12
4x + 18 = 7x
–4x –4x
18 = 3x
6 = x
Def. of bisector
Substitute the given values.
Add 12 to both sides.
Simplify.
Subtract 4x from both sides.
Divide both sides by 3.
Simplify.
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Example 4 Continued
Step 2 Find mJKM.
mJKM = 4x + 6
= 4(6) + 6
= 30
Substitute 6 for x.
Simplify.
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Assignment #4 pg 38-39
Foundation: 7 – 21
Core: 26, 28, 29, 33-36
Challenge: 40