Section 1-4 ANGLES

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

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

Example 1 What are two other names for angle 1? What is the vertex? Angle JMK Angle KMJ Cannot be angle M K J L 1 2 M

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 Obtuse Angle Acute Angle Right Angle Straight Angle Exterior Angle

On a Protractor A protractor is a device that measures an interior angle Vertex goes here

Protractor Formula C D O Answer is 60°

Protractor Formula C D O Answer is 50°

The Sprinkle of Algebra Angle Addition Postulate If angle AOB = 35° If angle BOC = 20° What is angle AOC? 55° 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 C 11x - 12 2x + 10 E D F

Assignment Pg 31 -32 6 – 23 29 & 30