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Angle Measures and Angle Bisectors

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by

Juan Jorrin

on 4 February 2019

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Transcript of Angle Measures and Angle Bisectors

Angle Bisector
Angles can be measured using degrees and radians.
Vertex
Angle Measures and Angle Bisectors
Classifying angles by measurement
Angle
1. Find
x
if
ABC
is bisected by BD.
Angle Addition Postulate
2. Use the figure to find the measure of the angle
ZXY
if angle
WXY
measures
138°
and angle
WXZ
is a right angle.
A
B
C
Sides
Rays
AB

and
BC
are connected by a common
endpoint B.
The figure formed is called an
angle
.
common endpoint
two rays
Angles can be named using:
ABC
CBA
or
B
is Vertex
3 letters, which corresponds to the 3 points. The middle letter is the vertex.
a single letter (or number) that corresponds to the vertex
B
or
One full rotation or one complete circle is 360°, then 1° angle is equivalent to 1/360 of a circle.
Example: If angle
A
= 30°, then the measurement can be written as m
A
= 30°
Classification of Angles
Angles can be classified by their angle measurement.
Acute Angle
Right Angle
Obtuse Angle
Straight Angle
Acute Angle
RIght Angle
Obtuse Angle
Straight Angle
Ɵ
90°
Ɵ
180°
measures less than 90°
measures 90°
measures more than 90°, but less than 180°
measures 180°
P
Q
R
S
A ray that splits the angle in two equal angles is called the
angle bisector
.
PQR
is bisected by
QS
then
m
PQS =
m
SQR
A
B
C
D
4
x
+ 1
This symbol means that the angle is a right angle.
m
ABC
= 90°
BD
is an angle bisector, then it only means that it divides
ABC
into 2 equal angles.
45°
45°
m
ABD
= 45°
m
DBC
= 45°
Substitute m ABD = 4x + 1.
4
x
+ 1
= 45°
Subtract both sides by 1.
4
x
+ 1
- 1
= 45°
- 1
4
x
= 44°
Divide both sides by 4.
4
4
x
= 11°
Given that point
D
is inside
ABC
.
A
B
C
D
A ray is drawn from
B
to
D
.
ABC
is split into two parts,
ABD
and
DBC
.
Angle Addition states that
m
ABC
= m
ABD
+ m
DBC
W
X
Y
Z
90°
Apply the angle addition postulate.
m
WXY =
m
WXZ +
m
ZXY
Substitute the given values:
138°
=
90°
+ m ZXY
Solve for angle ZXY by subtracting both sides by 90°.
138°
- 90°

=
90°

- 90°
+ m ZXY
Simplify and switch sides.
m
ZXY
= 48°
(5
x
- 8)°
(3
x
- 4)°
3. Find the measure of angle
EFH
and angle
HFG
, if angle
EFG
is 156°.
E
F
G
H
Apply the angle addition postulate.
m
EFG =
m
EFH +
m
HFG
Substitute the given values.
Identify the given.
m
EFG =
156
°
m
EFH =
(3
x -
4)°
m
HFG =
(5
x -
8)°
156° = (3
x
- 4)° + (5
x
- 8)°
Combine like terms.
156° = 8
x
- 12°
156°
+ 12°
= 8
x
- 12°
+ 12°
8
x
= 168°
8
8
x
= 21°
Add both sides by 12 .
Simplify and switch sides.
Divide both sides by 8.
Use x = 21 to find m EFH and m HFG.
m
EFG =
(3
x
- 4)°
m
HFG =
(5
x
- 8)°
=
(3
21
- 4)°
=
(5
21
- 8)°
=
(
63
- 4)°
m
EFG =
59°
=
(
105
- 8)°
m
HFG =
97°
Check by plugging our answers on the equation:
m
EFG =
m
EFH +
m
HFG
156° = 59° + 97°
156° = 156°
This statement is true, then our answers are correct!
Full transcript