Identify linear pair, vertical angles, complementary and supplementary angles, and solve problems.

1. Pairs of Angles
Objectives:
The student will be able to (I can):
Classify angles as acute, right, or obtuse
Identify
• linear pairs
• vertical angles
• complementary angles
• supplementary angles
and set up and solve equations.

2. acute angle
right angle
obtuse angle
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.

3. congruent
angles
Angles that have the same measure.
m∠WIN = m∠LHS
∠WIN ≅ ∠LHS
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”
●●
●
● ●
●
L
H
S
W
IN

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

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

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

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

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

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

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

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

12. adjacent
angles
linear pair
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.
Two adjacent angles whose noncommon
sides are opposite rays. (They form a line.)
Example:
1
2

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

14. 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)
A
55º
B
35º
C
125º

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

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

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

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