**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!