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.
m1 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
m1 = 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 mTQP + m RQS = 47° + 43° = 90°
EX5) Name two pairs of supplementary angles.
TQP, RQT mTQP + m RQT = 47° + 133° = 180°
SQP, SQR mSQP + m SQR = 137° + 43° = 180°
Assignment
Page 593 4-11
Page 601 1-6