Do Now (Turn on laptop to my calendar)
Simplify each expression.
1. 90 – (x + 20) 70 – x
2. 180 – (3x – 10) 190 – 3x
Write an algebraic expression for each of the
following.
3. 4 more than twice a number 2n + 4
4. 6 less than half a number
Do Now (Turn on laptop to my calendar)
Simplify each expression.
1. 90 – (x + 20)
2. 180 – (3x – 10)
Success Criteria:

I can identify special angle pairs

I can identify geometric relationships

I can use angle pairs to find angle
measures
Today
1. Do Now
2. Check HW #3
3. Vocabulary
4. Lesson 1.5
5. HW #4
6. Complete iReady
Vocabulary
adjacent angles
linear pair
complementary angles
supplementary angles
vertical angles
Angle bisector
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.
Example 1: Identifying Angle Pairs
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not adjacent.
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
Tell whether the angles are only adjacent,
adjacent and form a linear pair, or not
adjacent.
5 and 6
5 and 6 are adjacent angles. Their
noncommon sides, EA and ED, are opposite
rays, so 5 and 6 also form a linear pair.
Example 3: Finding the Measures of
Complements and Supplements
Find the measure of each of the following.
A. complement of F
(90 – x)
90 – 59 = 31
B. supplement of G
(180 – x)
180 – (7x+10) = 180 – 7x – 10
= (170 – 7x)
Example 4: Finding the Measure of an Angle
Copy the image and label it!!!
KM bisects JKL, mJKM = (4x + 6)°,
and mMKL = (7x – 12)°.
Find mJKM.
Example 4 Solution
Step 1 Find x.
mJKM = mMKL
Def. of  bisector
(4x + 6)° = (7x – 12)°
+12
+12
4x + 18
–4x
= 7x
–4x
18 = 3x
6=x
Substitute the given values.
Add 12 to both sides.
Simplify.
Subtract 4x from both sides.
Divide both sides by 3.
Simplify.
Step 2 Find mJKM.
mJKM = 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
mHML  mJMK  60°.
mHMJ  mLMK  120°.
Do Now Can you pass this quiz?
mXYZ = 2x° and mPQR = (8x - 20)°.
1. If XYZ and PQR are supplementary,
find the measure of each angle.
40°; 140°
2. If XYZ and PQR are complementary,
find the measure of each angle.
22°; 68°
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 mXYV is 8x + 10 and
mZYV is 12x – 6. Draw a picture, label the
picture and find the value of x.
x=4
2. mXYZ = 2x° and mPQR = (8x - 20)°.
If XYZ and PQR are complementary, find
the measure of each angle.
22°; 68°
Check It Out! Example 4
What if...? Suppose m3 = 27.6°. Find
m1, m2, and m4.
2
Make a Plan
If 1  2, then m1 = m2.
If 3 and 1 are complementary,
then m1 = (90 – 27.6)°.
If 4 and 2 are complementary,
then m4 = (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.
• m3 = 27.6°
3
Solve
By the Transitive Property of Equality, if
m1 = 62.4° and m1 = m2, then
m2 = 62.4°.
Since 3 and 1 are complementary,
m3 = 27.6°. Similarly, since 2 and 4 are
complementary, m4 = 27.6°.
4
Look Back
The answer makes sense because
27.6° + 62.4° = 90°, so 1 and 3 are
complementary, and 2 and 4 are
complementary.
Thus m1 = m2 = 62.4°; m4 = 27.6°.