Section 1-4

Points to Clarify

Angles and sides are not friends Do not speak the same language Do not have the same properties Therefore, do NOT use an angle to solve

for a side and vice versa That is what trigonometry is for

What is an Angle?

An angle is two rays that share an endpoint The shared endpoint is called the vertex

The vertex here is A The two rays are called sides

A

B

C

AB AC

Naming Angles

There are 3 ways to name angles By the vertex alone

By the number given

By the three points that comprise the

angle Be sure the vertex is in the middle or

A

B

C

2

A

2

BAC CAB

Example 1

What are two other names for angle 1? What is the vertex?

M Angle JMK Angle KMJ

Cannot be angle M

M

J K

L

1 2

Types of Angles

You were used to three types of angles I teach five types Acute Angles

Any angle that measures between 0 and 90 degrees

Right Angles Any angle that measures exactly 90

degrees Usually indicated by a small red square

next to the vertex

Types of Angles

Obtuse Angles Any angle that measures between 90 and 180

degrees The previous three types all measure

what is called the interior of an angle Straight Angle

Any angle that measures exactly 180 degrees Also referred to as opposite rays

Exterior Angles Any angle that measures between 180 and

360 degrees

Types of Angles

Acute Angle

Right Angle

Obtuse Angle

Straight Angle Exterior Angle

On a Protractor A protractor is a device that

measures an interior angle

Vertex goes here

Protractor Formula

dcCOD

Answer is 60°

C

DO

Protractor Formula

dcCOD

Answer is 50°

C

D

O

The Sprinkle of Algebra

Angle Addition Postulate

If angle AOB = 35° If angle BOC = 20° What is angle AOC?

55°

AOCBOCAOB

O

A

B

C

The Sprinkle of Algebra

Find angle AOB and BOC Angle AOB = 4x – 20 Angle BOC = 3x + 14 Angle AOC = 155°

Use Angle Addition Postulate 4x – 20 + 3x + 14 = 155 7x – 6 = 155 + 6 + 6 7x = 161 7 7 x = 23

O

A

B

C

The Sprinkle of Algebra

Partner Up and try Angle DEF is a straight angle Angle DEC = 11x – 12 Angle CEF = 2x + 10 Find Angle DEC and CEF

11x - 12

2x + 10D

C

E F

Assignment

Pg 31 -32 6 – 23 29 & 30