Transcript Document
Angle Relationships with
Complementary and
Supplementary Angles
A ray is a part of a
line that starts at
one point and
extends forever in
one direction.
J
K
M
Parallel lines are two
lines that never
cross
Perpendicular lines
are two lines that
form a 900 angle.
KJ
N
J
K
T
A
M
H
Quick review
not in notes
An angle () is formed by two rays with a
common endpoint called the vertex (plural,
vertices). Angles can be measured in degrees.
m1 means the measure of 1. The angle can
be named XYZ, ZYX, 1, or Y. The vertex
must be the middle letter.
X
Quick review
not in notes
Y
1
Z
m1 = 50°
The measures of angles that fit together to form
a straight line, such as FKG, GKH, and HKJ,
add to 180°.
E
G
H
F
K
J
A right angle measures 90°.
An acute angle measures less than 90°.
An obtuse angle measures greater than 90°
and less than 180°.
Complementary angles have measures that
add to 90°.
Supplementary angles have measures that
add to 180°.
T
EX1) Name the angle.
TQS
SQT
Q
1
Q
1
right
S
EX2) Name the angle.
ZJK KJZ J
2
acute
EX3) Name the angle.
VBH HBV B 3
J
.
.
2
K
V
3
obtuse
EX4) Name the angle.
FMN NMF M 4
.
Z
B
.
F
straight
H
.
M
4
.
N
Vertical Angles - Opposite Angles
1 & 3
2 & 4
Adjacent Angles - Touching Angles. Common vertex
and side. No overlap.
1 & 2
3 & 4
1 & 4
2 & 3
1
2
4
3
EX 7) Find X
2x + 15 = 75
- 15 - 15
2x
2
= 60
2
x
= 30
(2x + 15)○
75○
We know these angles are
vertical so they are
congruent (
)
EX4) Name a pair of complementary angles.
TQP, RQS mTQP + m RQS = 47° + 43° = 90°
EX5) Name two pairs of supplementary angles.
TQP, RQT mTQP + m RQT = 47° + 133° = 180°
SQP, SQR mSQP + m SQR = 137° + 43° = 180°
Assignment
Page 593 4-11
Page 601 1-6