1.5: Describe Angle Pair Relationships
Objectives:
1. To use special angle
relationships to find
angle measures
Assignment:
• P. 38-41: 2-20 even,
21, 28, 29, 32, 40, 45,
57, 58
• Challenge Problems
Objective 1
You will be able
to use special
angle
relationships to
find angle
measures
C Comes Before S…
m1  m2  90
m3  m4  90
m5  m6  180
m7  m8  180
Exercise 1a
1. Given that ∠1 is a complement of ∠2 and
𝑚∠1 = 68°, find 𝑚∠2.
2. Given that ∠3 is a supplement of ∠4 and
𝑚∠3 = 56°, find 𝑚∠4.
Exercise 1b
1. What is the sum of complementary angles
in radians?
2. What is the sum of supplementary angles
in radians?
3. What is complement for the angle that
measures 𝜋/3?
4. What is the supplement for the angle that
measures 3𝜋/4?
Exercise 2
Let ∠𝐴 and ∠𝐵 be complementary angles
and let 𝑚∠𝐴 = 2𝑥 2 + 35 ° and
𝑚∠𝐵 = 𝑥 + 10 ° . What is (are) the
value(s) of 𝑥? What are the measures of
the angles?
Adjacent Angles
Two angles are
adjacent angles if they
share a common
vertex and a common
side but no common
interior points
∠𝐴𝐷𝐽 and ∠𝐽𝐷𝐶 are adjacent
∠𝐴𝐷𝐽 and ∠𝐴𝐷𝐶 are nonadjacent
Linear Pairs of Angles
Linear Pairs of Angles
Two adjacent angles
form a linear pair if their
noncommon sides form a
line.
The angles in a
linear pair are
supplementary
Vertical Angles
Vertical Angles
Two nonadjacent angles
are vertical angles if
their sides form two pairs
of opposite rays.
Vertical angles are
formed by two
intersecting lines.
Vertical Angles
Two nonadjacent angles
are vertical angles if
their sides form two pairs
of opposite rays.
Exercise 3
Identify all of the linear pairs of angles and all
of the vertical angles in the figure.
Exercise 4: SAT
y
z
In the figure  5 and  4 , what is the value
x
x
of x?
x
y
z
1.5: Describe Angle Pair Relationships
Objectives:
1. To use special angle
relationships to find
angle measures
Assignment:
• P. 38-41: 2-20 even,
21, 28, 29, 32, 40, 45,
57, 58
• Challenge Problems