Angle
Relationships
90 and 180 degree
angles……
• 90 degree angle:
• 180 degree angle:
Types of angles……
• Acute – angles less
than 90 degrees.
• Right – angles with
exactly 90
degrees.
• Obtuse – angles
greater than 90
degrees but less
than 180 degrees.
• Straight – angles
that are 180
degrees and form a
line.
Identify these angles…..
• A.
• A. Obtuse
• B.
• B.
Right
• C.
• C.
Acute
• D.
• D.
Straight
Adjacent Angles……
• Two angles that share a common
side are adjacent angles.
• Example:
Non-adjacent Angles……
• Angles that do not share a common
side are non-adjacent angles.
• Example:
Supplementary
• Two angles whose sum is 180.
Complementary
• Two angles whose sum is 90.
Perpendicular
• If 2 segments are
perpendicular to
each other, then
they form a 90
degree angle.
• The symbol for
perpendicular is an
upside down T.

• Example:
jk
Therefore, the 2 angles
must add up to 90 .
Let’s finish this
problem...Remember that j  k
2 x  x  90
60
3x  90
30
Find x and the value of
each angle.
x  30
2 x  230  60
Find x, given that
f g
5 x  10  25  90
5 x  35  90
5 x  55
x  11
Vertical Angles……
• Vertical Angles are
two non-adjacent
angles formed by
intersecting lines.
• Vertical Angles are
congruent. (Equal)
1 and2 are vertical angles.
So, m1  m2
3 and 4 are vertical angles.
So, m3  m4
Example……
• Find the value of x.
x  5  68
x  63
Example…..
• Find the mPQR
10 x  8 x  24
2 x  24
x  12
mPQR  10 x  10(12)  120
Linear Pairs
Linear Pair – a pair of adjacent angles whose non-common
sides form opposite rays.
1
2
∠1 and ∠2 form a linear pair.
A linear pair is supplementary – the angle measures
add up to 180 degrees.
Find x:
5 x  x  180
6 x  180
x  30
Homework
• Angle Relationships Worksheet