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Section 2-5: Angle Pairs
SPI 32E: solve problems involving complementary, supplementary,
congruent, vertical or adjacent angles given angle measures
expressed algebraically.
Objectives:
• Identify angle pairs
• Prove and apply theorems about angles
FOUR TYPES OF ANGLE PAIRS
Vertical Angles
Two angles whose sides are
opposite rays.
Adjacent Angles
Two coplanar angles with a
common side, a common vertex,
and no common interior points
Complementary Angles
• Two angles whose measures
have the sum of 90.
• Each angle is called the
complement of the other.
Supplementary Angles
• Two angles whose measures
have the sum of 180.
• Each angle is called the
supplement of the other.
Identify the Angle Pairs
Name all pairs of angles in the diagram that are:
a. vertical
Vertical angles are two angles whose sides are opposite rays.
Because all the angles shown are formed by two intersecting lines,
1 and 3 are vertical angles, and 2 and 4 are vertical angles.
b. supplementary
Two angles are supplementary if the sum of their measures is 180.
A straight angle has measure 180, and each pair of adjacent
angles in the diagram forms a straight angle. So these pairs of
angles are supplementary: 1 and 2, 2 and 3, 3 and 4,
and 4 and 1.
c. complementary
Two angles are complementary if the sum of their measures is 90.
No pair of angles is complementary.
Draw Conclusions from a Diagram
You can conclude that angles are:
• Adjacent Angles
• Adjacent supplementary
angles
• Vertical angles
Cannot conclude from a diagram unless there are markings:
• Angles and segments are 
• An angle is a right angle
• Lines are parallel or perpendicular
Angle Pairs
Use the diagram below. Which of the following can you conclude:
3 is a right angle, 1 and 5 are adjacent, 3  5?
You can conclude that 1 and 5 are adjacent
because they share a common side, a common
vertex, and no common interior points.
Although 3 appears to be a right angle, it is not marked
with a right angle symbol, so you cannot conclude that 3
is a right angle.
3 and 5 are not marked as congruent on the diagram. Although
they are opposite each other, they are not vertical angles. So you
cannot conclude that 3  5.
The vertical angles, as we found, measure 107º
107
107
What is the measure of the other pair of vertical angles? 73º
HELP!!
How do you know?
Think Definitions
Def: Adjacent angles are supplementary
and vertical angles are congruent
Use Algebra to find Angle Measures
Find the value of x.
Problem
Reason
4x – 101 = 2x + 3
Definition of Vertical Angles
4x = 2x + 104
Addition Property of Equality
2x = 104
Subtraction Property of Equality
x = 52
Division Property of Equality