Download What is an angle?

Sec 3.1
Angles & Angle
Measurements
Objective: What we’ll learn…
 Classify angles as acute,
obtuse, right, or straight.
 Measure/Draw angles by using
a protractor.
What is an angle?

Two rays that share the same endpoint form
an angle. The point where the rays intersect is
called the vertex of the angle. The two rays
are called the sides of the angle.
Here are some examples
of angles.
Naming an Angle
We can identify an angle
by using a point on
each ray and the
vertex. The angle
below may be identified
(Ray)
as angle ABC or as
angle CBA; you may
also see this written as
(Ray)
< ABC or as < CBA.
(VERTEX)
The vertex point is
always in the middle.
Degrees: Measuring Angles
We measure the size of an angle using degrees.
Example: Here are some examples of angles and
their degree measurements.
Protractor
A device used to measure angles.
Reading a Protractor
Date: 9/8/96 at 22:29:58 From: Bob Vanselow
Subject: Reading a Protractor Which side of a protractor scale do
you use?
Date: 9/9/96 at 11:39:23 From: Doctor Robert
Subject: Re: Reading a Protractor
I think that the easiest way to decide which scale to use is to look at the angle
you're measuring. If it is greater than a right angle (more than ninety degrees)
then use the scale that has numbers greater than 90. If the angle is obviously
acute (measures less than 90 degrees), use the scale which has numbers
less than 90. Of course you have to line up the protractor correctly with
the center point on the vertex of the angle and one of the rays of the angle
coincide with the line on the protractor. Happy measuring!
-Doctor Robert, The Math Forum Check out our web site!
http://mathforum.org/dr.math/
Acute Angles
An acute angle is an angle measuring between 0
and 90 degrees.
Example:
Acute Angles
An acute angle is an angle measuring between 0 and
90 degrees.
Task:
Draw the following acute angles in your
notes.
1) 72o
2) 60o
3) 51.5o
4) 45o
5) 40o
6) 36o
Obtuse Angles
An obtuse angle is an angle measuring between 90 and
180 degrees.
Example:
Obtuse Angles
An obtuse angle is an angle measuring between 90 and
180 degrees.
Task:
Draw the following obtuse angles in your
notes.
1) 120o
2) 150o
3) 135o
4) 170o
5) 100o
6) 95o
Right Angles
A right angle is an angle measuring 90 degrees.
Examples:
Straight Angles
A straight angle is an angle measuring 180 degrees.
Examples:
Review
State whether the following are acute, right, or obtuse.
1.
3.
5.
acute
obtuse
right
2.
4.
?
acute
?
obtuse
Sec 3.2
Angles & Angle
Relationships
Complementary Angles
Two angles are called complementary angles if the
sum of their degree measurements equals 90 degrees.
Example:
These two angles are complementary.
These two angles can be "pasted"
together to form a right angle!
Supplementary Angles
Two angles are called supplementary angles if the sum
of their degree measurements equals 180 degrees.
Example:
These two angles are supplementary.
These two angles can be "pasted"
together to form a straight line!
Vertical Angles
2
two angles…
1
2
1)share a vertex
2)are directly across from each other
3)created by two crossing lines.
Vertical Angles are congruent.
1
Vertical Angles
For any two lines that meet, such as in the diagram below,
AEB and DEC are called vertical angles.
BEC and AED are also vertical angles.
Vertical angles have the same degree
measurement.
Linear Pair
Two angles…
1)share a vertex
2)form a straight line (add to 180° or supplementary)
3)must be ADJACENT (next to each other)
Complementary and
Supplementary
Find the missing angle.
1. Two angles are complementary. One measures 65 degrees.
Answer : 25
2. Two angles are supplementary. One measures 140 degrees.
Answer : 40
Complementary and
Supplementary
Find the missing angle. You do not have a protractor.
Use the clues in the pictures.
1.
2.
x
x
55
165
X=35
X=15
Vertical Angles
Find the missing angle. You do not have a protractor.
Use the clues in the pictures.
x
58
X=58
More drawings
F
E
20
70
90
D
G
C
70
J
90
20
H
Final Drawing
B
C
68
A
52
60
G
D
52
60
68
F
E