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Simplify each expression.

1. 90 – (x + 20)

2. 180 – (3x – 10)

70 – x

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)

Identify special angle pairs and use their relationships and find angle measures.

Target

Chapter 1-5 Exploring Angle Pairs

adjacent angleslinear pairvertical anglescomplementary anglessupplementary anglesangle bisector

Vocabulary

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

An angle bisector is a ray that divides an angle into two congruent angles.

JK bisects LJM; thus LJK KJM.

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

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.

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?

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

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)

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

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.

Example 4 Continued

Step 2 Find mJKM.

mJKM = 4x + 6

= 4(6) + 6

= 30

Substitute 6 for x.

Simplify.

Assignment #4 pg 38-39

Foundation: 7 – 21

Core: 26, 28, 29, 33-36

Challenge: 40