Angle Measure (Geometry 3_2)
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Transcript of Angle Measure (Geometry 3_2)
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You will learn to measure, draw, and classify angles.
1) Degrees2) Protractor3) Right Angle4) Acute Angle5) Obtuse Angle
Angle MeasureAngle Measure
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In geometry, angles are measured in units called _______.degrees
Angle MeasureAngle Measure
![Page 3: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/3.jpg)
In geometry, angles are measured in units called _______.degrees
The symbol for degree is °.
Angle MeasureAngle Measure
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In geometry, angles are measured in units called _______.degrees
The symbol for degree is °.
Q
P
R
75°
In the figure to the right, the angle is 75 degrees.
In notation, there is no degree symbol with 75because the measure of an angle is a real number with no unit of measure.
m PQR = 75
Angle MeasureAngle Measure
![Page 5: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/5.jpg)
Postulate 3-1
Angles Measure Postulate
For every angle, there is a unique positive number between __ and ____ called the degree measure of the angle.
B
A
C
n°
Angle MeasureAngle Measure
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Postulate 3-1
Angles Measure Postulate
For every angle, there is a unique positive number between __ and ____ called the degree measure of the angle.
B
A
C
n°
0
Angle MeasureAngle Measure
![Page 7: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/7.jpg)
Postulate 3-1
Angles Measure Postulate
For every angle, there is a unique positive number between __ and ____ called the degree measure of the angle.
B
A
C
n°
0 180
Angle MeasureAngle Measure
![Page 8: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/8.jpg)
Postulate 3-1
Angles Measure Postulate
For every angle, there is a unique positive number between __ and ____ called the degree measure of the angle.
B
A
C
n°
0 180
m ABC = nand 0 < n < 180
Angle MeasureAngle Measure
![Page 9: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/9.jpg)
J
H
G
SQ R
m SRQ =
Find the measurement of:
m SRJ =
m SRG =
m QRG =
m GRJ =
m SRH
Angle MeasureAngle Measure
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J
H
G
SQ R
m SRQ =
Find the measurement of:
m SRJ =
m SRG =
m QRG =
m GRJ =
180
45
150
70
180 – 150= 30
150 – 45= 105
m SRH
Angle MeasureAngle Measure
![Page 11: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/11.jpg)
Use a protractor to draw an angle having a measure of 135.
Angle MeasureAngle Measure
![Page 12: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/12.jpg)
Use a protractor to draw an angle having a measure of 135.
1) Draw AB
A B
Angle MeasureAngle Measure
![Page 13: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/13.jpg)
Use a protractor to draw an angle having a measure of 135.
1) Draw AB
2) Place the center point of the protractor on A. Align the mark labeled 0 with the ray.
A B
Angle MeasureAngle Measure
![Page 14: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/14.jpg)
Use a protractor to draw an angle having a measure of 135.
1) Draw AB
2) Place the center point of the protractor on A. Align the mark labeled 0 with the ray.
3) Locate and draw point C at the mark labeled 135. Draw AC.
A B
Angle MeasureAngle Measure
![Page 15: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/15.jpg)
Use a protractor to draw an angle having a measure of 135.
1) Draw AB
2) Place the center point of the protractor on A. Align the mark labeled 0 with the ray.
3) Locate and draw point C at the mark labeled 135. Draw AC.
C
A B
Angle MeasureAngle Measure
![Page 16: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/16.jpg)
Once the measure of an angle is known, the angle can be classified as oneof three types of angles. These types are defined in relation to a right angle.
Angle MeasureAngle Measure
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Once the measure of an angle is known, the angle can be classified as oneof three types of angles. These types are defined in relation to a right angle.
Types of Angles
A
Angle MeasureAngle Measure
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Once the measure of an angle is known, the angle can be classified as oneof three types of angles. These types are defined in relation to a right angle.
Types of Angles
obtuse angle 90 < m A < 180
A
Angle MeasureAngle Measure
![Page 19: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/19.jpg)
Once the measure of an angle is known, the angle can be classified as oneof three types of angles. These types are defined in relation to a right angle.
Types of Angles
A
obtuse angle 90 < m A < 180
A
Angle MeasureAngle Measure
![Page 20: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/20.jpg)
Once the measure of an angle is known, the angle can be classified as oneof three types of angles. These types are defined in relation to a right angle.
Types of Angles
A
right angle m A = 90
obtuse angle 90 < m A < 180
A
Angle MeasureAngle Measure
![Page 21: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/21.jpg)
Once the measure of an angle is known, the angle can be classified as oneof three types of angles. These types are defined in relation to a right angle.
Types of Angles
A
right angle m A = 90
A
obtuse angle 90 < m A < 180
A
Angle MeasureAngle Measure
![Page 22: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/22.jpg)
Once the measure of an angle is known, the angle can be classified as oneof three types of angles. These types are defined in relation to a right angle.
Types of Angles
A
right angle m A = 90
acute angle 0 < m A < 90
A
obtuse angle 90 < m A < 180
A
Angle MeasureAngle Measure
![Page 23: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/23.jpg)
Classify each angle as acute, obtuse, or right.
110°
90°40°
50°
130° 75°
Angle MeasureAngle Measure
![Page 24: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/24.jpg)
Classify each angle as acute, obtuse, or right.
110°
90°40°
50°
130° 75°
Obtuse
Obtuse
Acute
Acute Acute
Right
Angle MeasureAngle Measure
![Page 25: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/25.jpg)
5x - 7
B
The measure of B is 138.Solve for x.
Angle MeasureAngle Measure
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5x - 7
B
The measure of B is 138.Solve for x.
B = 5x – 7 and B = 138
Given: (What do you know?)
Angle MeasureAngle Measure
![Page 27: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/27.jpg)
5x - 7
B
The measure of B is 138.Solve for x.
B = 5x – 7 and B = 138
Given: (What do you know?)
5x – 7 = 138
5x = 145
x = 29
Angle MeasureAngle Measure
![Page 28: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/28.jpg)
5x - 7
B
The measure of B is 138.Solve for x.
B = 5x – 7 and B = 138
Given: (What do you know?)
5x – 7 = 138
5x = 145
x = 295(29) -7 = ?
145 -7 = ?
138 = 138
Check!
Angle MeasureAngle Measure
![Page 29: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/29.jpg)
9y + 4H
The measure of H is 67.Solve for y.
Angle MeasureAngle Measure
![Page 30: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/30.jpg)
9y + 4H
The measure of H is 67.Solve for y.
H = 9y + 4 and H = 67
Given: (What do you know?)
Angle MeasureAngle Measure
![Page 31: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/31.jpg)
9y + 4H
The measure of H is 67.Solve for y.
H = 9y + 4 and H = 67
Given: (What do you know?)
9y + 4 = 67
9y = 63
y = 7
Angle MeasureAngle Measure
![Page 32: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/32.jpg)
9y + 4H
The measure of H is 67.Solve for y.
H = 9y + 4 and H = 67
Given: (What do you know?)
9y + 4 = 67
9y = 63
y = 79(7) + 4 = ?
63 + 4 = ?
67 = 67
Check!
Angle MeasureAngle Measure
![Page 33: Angle Measure (Geometry 3_2)](https://reader036.fdocuments.us/reader036/viewer/2022081416/55614be3d8b42a780d8b4a0a/html5/thumbnails/33.jpg)
Angle MeasureAngle Measure