ADJACENT,
VERTICAL,
SUPPLEMENTARY, AND
COMPLEMENTARY ANGLES
LINEAR PAIR,
PERPENDICULAR LINES

Adjacent angles are “side by side” and share a common ray.
45º
15º

These are examples of adjacent angles.
80º
45º
35º
55º
85º
20º
130º 50º

These angles are NOT adjacent.
100º
50º
35º
35º
55º 45º

When 2 lines intersect, they make vertical angles.
105º
75º
105º
75º

Vertical angles are opposite from one another.
105º
75º
105º
75º

Vertical angles are opposite from one another.
105º
75º
105º
75º

Vertical angles are congruent (equal).
30º
150º
150º
30º

Supplementary angles add up to 180º.
120º 60º
Adjacent and Supplementary
Angles
40º
140º
Supplementary Angles but not Adjacent

Complementary angles add up to 90º.
30º
60º
Adjacent and Complementary
Angles
40º
50º
Complementary Angles but not Adjacent

Perpendicular Lines: intersect to form four right angles

Practice Time!

Practice
Directions:
Identify each pair of angles as vertical, supplementary, complementary, linear pair or none of the above.

#1
120º
60º

#1
120º
60º
Supplementary Angles
Linear Pair

#2
30º
60º

#2
30º
60º
Complementary Angles

#3
75º
75º

#3
Vertical Angles
75º
75º

#4
40º
60º

#4
40º
60º
None of the above

#5
60º
60º

#5
60º
60º
Vertical Angles

#6
135º 45º

#6
135º 45º
Supplementary Angles
Linear Pair

#7
25º
65º

#7
25º
65º
Complementary Angles

#8
90º
50º

#8
90º
50º
None of the above

#1
?º 45º

#1
135º 45º

#2
?º
65º

#2
25º
65º

#3
35º
?º

#3
35º
35º

#4
?º
50º

#4
130º
50º

#5
?º
140º

140º
140º
#5

#6
?º
40º

50º
40º
#6



The Linear Pair Conjecture
Materials: paper, pencil, 2 sheets of patty paper & protractor
Draw line PQ and place a point R between P and Q.





Choose another point S not on line PQ and draw ray RS.
You have just create a linear pair of angles.
Place the “zero edge” of your protractor along line PQ.
What do you notice about the sum of the measures of the linear pair of angles?
Compare your results with those of your class. Does everyone make the same observation?
What is the Linear Pair Conjecture?
Example:




Vertical Angles Conjectures
Materials: paper, pencil, 2 sheets of patty paper & protractor
Fold patty paper, make a crease, outline the crease, place points A & B on the line.
Fold patty paper again so that you form intersecting lines, make a crease, outline the crease, place points D & E on the line and label the intersection C. (Make sure C is between A & B)



Which angles are vertical angles?
Fold the paper again through point C so that <ACD lies on top of <ECB. What do you notice?
What do you notice about their measures?


Your Turn…

Fold through C so that <ACE lies on DCB. What do you notice?

Compare your results with the class.

What is the Vertical Angles Conjecture?

Use a protractor to measure each angles. Write the measures on drawing.

Name the linear pairs. What do you notice about their measures?

Repeat this activity with another piece of patty paper. What do you notice?


Let’s Race!

Find a partner, get a deck of cards, and play “Say it faster!”

Whoever say the complement/supplement faster gets the pair of cards.

The person with the most cards, WINS!

10, Jacks, Queens, Kings, & Aces = 1

Every other find the complement or supplement.


Complete Angles Relationships

Complete Angle Addition

Quiz will be tomorrow

Study guide tomorrow

Test will be on Friday

Warm-Up: Identify each pair of angles
Use: adjacent, vertical, complementary, supplementary, and/or linear pair

1. <1 & <2
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2. <1 & <4 2 3
1

3. <4 & <5 5 4

4. <3 & <4

Find x and each measure

1. (5x+ 16)º
(6x + 8)º

3. (10x + 35)º
2.
(5x + 18)º
(7x + 12)º
(13x + 30)º
4. Ray BC is an angle bisector.
Find <CBD & <ABC. A
63º
B C
D

Find x and each measure

1. (5x+ 16)º
(6x + 8)º
2.
(5x + 18)º
(7x + 12)º

Find x and each measure

3. (10x + 35)º
(13x + 30)º
4. Ray BC is an angle bisector.
Find <CBD & ABC. A
63º
B C
D


1. The m < ABC = 6x – 8, m < ABD = 3x + 2, and m < DBC = 2x – 1. Find the measure of each angle.
A
B D
C


A I
C 1 2 S
B
3 4
T

1. Name angle 3.

2. < 3 & <4 are….
How to measure and construct angles?
How to analyze and measure pairs of angles?

3. If m < IBT is 135, find
<SBT.

4. <4 = 4x + 5 & <3 =
6x + 5. Find each measure.


Check study guide
How to measure and construct angles?
How to analyze and measure pairs of angles?

Any last minute questions before test