The student will be able to (I can): Correctly name an angle Classify angles as acute, right, or obtuse Identify linear pairs vertical angles complementary angles supplementary angles and set up and solve equations.

1. Obj. 8 Angles
Objectives:
The student will be able to (I can):
Correctly name an angle
Classify angles as acute, right, or obtuse
IdentifyIdentify
• linear pairs
• vertical angles
• complementary angles
• supplementary angles
and set up and solve equations.
Obj. 8 Angles
The student will be able to (I can):
Classify angles as acute, right, or obtuse
and set up and solve equations.

2. angle
vertex
A figure formed by two rays or sides with a
common endpoint.
Example:
The common endpoint of two rays or sides
(plural vertices(plural vertices
Example: A is the vertex of the above angle
A figure formed by two rays or sides with a
common endpoint.
The common endpoint of two rays or sides
vertices).
●
●
●
A
C
R
vertices).
Example: A is the vertex of the above angle

3. Notation: An angle is named one of three
different ways:
1. By the vertex and a point on each ray1. By the vertex and a point on each ray
(vertex must be in the middle) :
2. By its vertex (if only one angle):
3. By a number:
Notation: An angle is named one of three
different ways:
1. By the vertex and a point on each ray
●
●
● E
T
A
1
1. By the vertex and a point on each ray
(vertex must be in the middle) :
∠TEA or ∠AET
By its vertex (if only one angle): ∠E
3. By a number: ∠1

4. Example Which name is
below?
∠TRS∠TRS
∠SRT
∠RST
∠2
∠R
Which name is notnotnotnot correct for the angle
●
●
●
S R
T
2

5. Example Which name is
below?
∠TRS∠TRS
∠SRT
∠RST
∠2
∠R
Which name is notnotnotnot correct for the angle
●
●
●
S R
T
2

6. acute angle
right angle
Angle whose measure is greater than 0º
and less than 90º.
Angle whose measure is exactly 90º.
obtuse angle Angle whose measure is greater than 90º
and less than 180º.
Angle whose measure is greater than 0º
and less than 90º.
Angle whose measure is exactly 90º.
Angle whose measure is greater than 90º
and less than 180º.

7. congruent
angles
Angles that have the same measure.
m∠WIN = m∠
∠WIN ≅ ∠LHS
N
Notation: “Arc marks” indicate congruent
angles.
Notation: To write the measure of an angle,
put a lowercase “m” in front of the angle
bracket.
m∠WIN is read “measure of angle WIN”
Angles that have the same measure.
∠LHS
LHS
●●
●
● ●
●
L
H
S
W
IN
Notation: “Arc marks” indicate congruent
Notation: To write the measure of an angle,
put a lowercase “m” in front of the angle
WIN is read “measure of angle WIN”

8. interior of an
angle
Angle Addition
Postulate
The set of all points between the sides of
an angle
If D is in the interiorinteriorinteriorinterior
m∠ABD + m
(part + part = whole)
Example: If m
m∠
●
A
The set of all points between the sides of
interiorinteriorinteriorinterior of ∠ABC, then
ABD + m∠DBC = m∠ABC
(part + part = whole)
●
Example: If m∠ABD=50˚ and
∠ABC=110˚, then m∠DBC=60˚
●
●
●
B
D
C

9. Example The m∠PAH = 125˚.
●
P
(2x+8)
PAH = 125˚. Solve for x.
●
●
●
A
T
H
(3x+7)˚
(2x+8)˚

10. Example The m∠PAH = 125˚.
m∠PAT + m∠
●
P
(2x+8)
m∠PAT + m∠
PAH = 125˚. Solve for x.
∠TAH = m∠PAH
●
●
●
A
T
H
(3x+7)˚
(2x+8)˚
∠TAH = m∠PAH

11. Example The m∠PAH = 125˚.
m∠PAT + m∠
●
P
(2x+8)
m∠PAT + m∠
2x + 8 + 3x + 7 = 125
PAH = 125˚. Solve for x.
∠TAH = m∠PAH
●
●
●
A
T
H
(3x+7)˚
(2x+8)˚
∠TAH = m∠PAH
2x + 8 + 3x + 7 = 125

12. Example The m∠PAH = 125˚.
m∠PAT + m∠
●
P
(2x+8)
m∠PAT + m∠
2x + 8 + 3x + 7 = 125
5x + 15 = 125
PAH = 125˚. Solve for x.
∠TAH = m∠PAH
●
●
●
A
T
H
(3x+7)˚
(2x+8)˚
∠TAH = m∠PAH
2x + 8 + 3x + 7 = 125
5x + 15 = 125

13. Example The m∠PAH = 125˚.
m∠PAT + m∠
●
P
(2x+8)
m∠PAT + m∠
2x + 8 + 3x + 7 = 125
5x + 15 = 125
PAH = 125˚. Solve for x.
∠TAH = m∠PAH
●
●
●
A
T
H
(3x+7)˚
(2x+8)˚
∠TAH = m∠PAH
2x + 8 + 3x + 7 = 125
5x + 15 = 125
5x = 110

14. Example The m∠PAH = 125˚.
m∠PAT + m∠
●
P
(2x+8)
m∠PAT + m∠
2x + 8 + 3x + 7 = 125
5x + 15 = 125
PAH = 125˚. Solve for x.
∠TAH = m∠PAH
●
●
●
A
T
H
(3x+7)˚
(2x+8)˚
∠TAH = m∠PAH
2x + 8 + 3x + 7 = 125
5x + 15 = 125
5x = 110
x = 22

15. angle bisector A ray that divides an angle into two
congruent angles.
Example:
UY bisects ∠SUN; thusUY bisects ∠SUN; thus
A ray that divides an angle into two
congruent angles.
SUN; thus ∠SUY ≅ ∠YUN
●
●●
●
S
U
N
Y
SUN; thus ∠SUY ≅ ∠YUN
or m∠SUY = m∠YUN

16. adjacent
angles
Two angles in the same plane with a
common vertex and a common side, but no
common interior points.
Example:
∠1 and ∠2 are adjacent angles.
linear pair
∠1 and ∠2 are adjacent angles.
Two adjacent angles whose noncommon
sides are opposite rays. (They form a line.)
Example:
Two angles in the same plane with a
common vertex and a common side, but no
common interior points.
2 are adjacent angles.
1
2
2 are adjacent angles.
Two adjacent angles whose noncommon
sides are opposite rays. (They form a line.)

17. vertical angles Two nonadjacent angles formed by two
intersecting lines.
congruent.congruent.congruent.congruent.
Example:
∠1 and
∠2 and
Two nonadjacent angles formed by two
intersecting lines. They are alwaysThey are alwaysThey are alwaysThey are always
1
2
3
4
1 and ∠4 are vertical angles
2 and ∠3 are vertical angles

18. complementary
angles
supplementary
angles
Two angles whose measures have the sum
of 90º.
Two angles whose measures have the sum
of 180º.
∠A and ∠B are complementary. (55+35)
∠A and ∠C are supplementary. (55+125)
Two angles whose measures have the sum
Two angles whose measures have the sum
55º
35º
B are complementary. (55+35)
C are supplementary. (55+125)
A B
C
125º

19. Practice 1. What is m
2. What is m
3. What is m
What is m∠1?
What is m∠2?
1 60˚
What is m∠3?
51˚ 2
105˚
3

20. Practice 1. What is m
180 — 60 = 120
2. What is m
3. What is m
What is m∠1?
60 = 120˚
What is m∠2?
1 60˚
What is m∠3?
51˚ 2
105˚
3

21. Practice 1. What is m
180 — 60 = 120
2. What is m
90 — 51 = 39
3. What is m
What is m∠1?
60 = 120˚
What is m∠2?
51 = 39˚
1 60˚
What is m∠3?
51˚ 2
105˚
3

22. Practice 1. What is m
180 — 60 = 120
2. What is m
90 — 51 = 39
3. What is m
105˚
What is m∠1?
60 = 120˚
What is m∠2?
51 = 39˚
1 60˚
What is m∠3?
51˚ 2
105˚
3