Do Now (Turn on laptop to my calendar)Simplify each expression.

1. 90 – (x + 20)

2. 180 – (3x – 10)

Write an algebraic expression for each of the following.

3. 4 more than twice a number

4. 6 less than half a number

70 – x

190 – 3x

2n + 4

Chapter 1-5 Exploring Angle PairsI can identify special angle pairs and use their relationships

and find angle measures.

Success Criteria: I can identify special angle pairs I can identify geometric relationships I can use angle pairs to find angle

measures

Today1. Do Now 2. Check HW #33. Vocabulary4. Lesson 1.55. HW #46. Complete iReady

Do Now (Turn on laptop to my calendar)Simplify each expression.

1. 90 – (x + 20)

2. 180 – (3x – 10)

adjacent angleslinear paircomplementary anglessupplementary anglesvertical 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.

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

JK bisects LJM; thus LJK KJM.

Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.

Example 1: Identifying Angle Pairs

AEB and BED

AEB and BED have a common vertex, E, a common side, EB, and no common interior points. Their noncommon sides, EA and ED, are opposite rays. Therefore, AEB and BED are adjacent angles and form a linear pair.

Check It Out! Example 2

5 and 6

Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent.

5 and 6 are adjacent angles. Their noncommon sides, EA and ED, are opposite rays, so 5 and 6 also form a linear pair.

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 – x)180 – (7x+10) = 180 – 7x – 10

= (170 – 7x)

(90 – x)

Example 4: Finding the Measure of an Angle

Copy the image and label it!!!

KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°.

Find mJKM.

Example 4 SolutionStep 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.

Step 2 Find mJKM.

mJKM = 4x + 6

= 4(6) + 6

= 30 Substitute 6 for x.

Simplify.

Example 5: Identifying Vertical Angles

Name the pairs of vertical angles.

HML and JMK are vertical angles.HMJ and LMK are vertical angles.

Check mHML mJMK 60°.mHMJ mLMK 120°.

Do Now Can you pass this quiz?

mXYZ = 2x° and mPQR = (8x - 20)°.

1. If XYZ and PQR are supplementary, find the measure of each angle.

2. If XYZ and PQR are complementary, find the measure of each angle.

22°; 68°

40°; 140°

Assignment #4

pg 38#7-37odds 42-45, 47

Do Now – look at internet for learning target and complete do now in your new notebook

1. YV bisects XYZ and mXYV is 8x + 10 and mZYV is 12x – 6. Draw a picture, label the picture and find the value of x.

2. mXYZ = 2x° and mPQR = (8x - 20)°. If XYZ and PQR are complementary, find the measure of each angle.

22°; 68°

x = 4

What if...? Suppose m3 = 27.6°. Find m1, m2, and m4.

Check It Out! Example 4

2 Make a Plan

If 1 2, then m1 = m2.

If 3 and 1 are complementary, then m1 = (90 – 27.6)°.

If 4 and 2 are complementary, then m4 = (90 – 27.6)°.

1 Understand the Problem

The answers are the measures of 1, 2, and 4.

List the important information:

• 1 2• 1 and 3 are complementary, and 2 and 4 are complementary.• m3 = 27.6°

Solve3

By the Transitive Property of Equality, if m1 = 62.4° and m1 = m2, thenm2 = 62.4°.

Since 3 and 1 are complementary, m3 = 27.6°. Similarly, since 2 and 4 are complementary, m4 = 27.6°.

Look Back4

The answer makes sense because 27.6° + 62.4° = 90°, so 1 and 3 are complementary, and 2 and 4 are complementary.

Thus m1 = m2 = 62.4°; m4 = 27.6°.