Transcript 1.6 Measuring Angles

To measure angles
using a protractor.
To draw angles using a
protractor.
Different types of angles
In geometry, angles are
measured in units called
degrees
_______.
The symbol for degree is °.
In the figure below, the angle is
75 degrees.
P
Q
75°
R
Now, let’s measure an angle using a protractor.
Use a protractor to measure
SRQ.
1) Place the center point of the protractor
on vertex R.
Align the straightedge with side RS.
2) Use the scale that begins with 0
at RS.
Read where the other side
of the angle, RQ, crosses
this scale.
Q
1200
R
S
Let’s measure the following
angles.
Find the measurement of:
m
SRQ = 180
m
SRJ = 45
m
SRG = 150
H
J
G
Q
R
S
Let’s measure an angles

m
SRH
70
m
QRG = 180 – 150
= 30
m
GRJ = 150 – 45
= 105
H
J
G
Q
R
S
Try this one.
Use a protractor to draw an angle having a measure of 135.
1) Draw AB
3) Locate and draw point C at the
mark labeled 135. Draw AC.
2) Place the center point of the
protractor on A. Align the mark
labeled 0 with the ray.
C
A
B
Lets look at some
angles.
acute angle:
less than 900
obtuse angle:
more than 900
right angle:
900
straight angle:
1800
Classify each angle as acute,
obtuse, or right.
110°
40°
90°
Obtuse
Right
Acute
50°
130°
Acute
Obtuse
75°
Acute
Let’s use Algebra to answer the following.
The measure of
Solve for x.
B is 138.
5x - 7
B
Given:
(What do you know?)
B = 5x – 7 and
5x – 7 = 138
5x = 145
x = 29
B = 138
Check!
5(29) -7 = ?
145 -7 = ?
138 = 138
Here’s another one.
The measure of
Solve for y.
H is 67.
H
9y + 4
Given:
(What do you know?)
H = 9y + 4 and
9y + 4 = 67
9y = 63
y=7
H = 67
Check!
9(7) + 4 = ?
63 + 4 = ?
67 = 67
Is m
a
a larger than m
60°
b?
b
60°
Let’s try something different.
1) Draw an acute,
an obtuse, or
a right angle.
Label the
angle RST.
R
45°
2) Draw and label
a point X in the
interior of the
angle. Then
draw SX.
X
75°
S
3) For each angle, find mRSX, mXST, and RST.
30°
T
Here are some more
types of angles.
congruent angles:
vertical angles:
opposite angles
adjacent angles:
Here are some questions.
Determine whether 1 and 2 are adjacent angles.
No. They have a common
vertex B, but
no common side
_____________
2
1
B
1
Yes. They have the same vertex G and a
common side with no interior points in
common.
2
G
N
L
J
2
1
No. They do not have a common vertex or
a common side
____________
LN
The side of 1 is ____
JN
The side of 2 is ____
Let’s try something different.
Determine whether 1 and 2 are adjacent angles.
No.
1
2
Yes.
1
X
2
D
Z
In this example, the noncommon sides of the adjacent angles form a
straight line
___________.
linear pair
These angles are called a _________
Let’s try something different.
Find the value of x in the figure:
130°
x°
The angles are vertical angles.
So, the value of x is 130°.
Let’s try something different.
Find the value of x in the figure:
(x – 10)°
125°
The angles are vertical angles.
(x – 10) = 125.
x – 10 = 125.
x = 135.
Assignment
1.6 Measuring Angles
Geometry
Draw the following angles.
1. 500
2. 750
3. 1350
4. 1150
G
5. If m1 = 2x + 3 and the m3 = 3x + 2, then find the m3
D
1
6. If mABD = 4x + 5 and the mDBC = 2x + 1, then find the mEBC
A
4
7. If m1 = 4x - 13 and the m3 = 2x + 19, then find the m4
3
B
E
8. If mEBG = 7x + 11 and the mEBH = 2x + 7, then find the m1
H
2
C
???