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Understanding Angles and Their Properties for Trigonometry

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Learn about angles, their definitions, naming conventions, types (acute, obtuse, right, straight, exterior), use of protractor, algebraic angle addition postulate, and solve angle exercises. Improve your math skills!

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Understanding Angles and Their Properties for Trigonometry

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  1. Section 1-4 ANGLES

  2. 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

  3. 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 B A C

  4. 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 2 B A C

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

  6. 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

  7. 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

  8. Types of Angles Obtuse Angle Acute Angle Right Angle Straight Angle Exterior Angle

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

  10. Protractor Formula C D O Answer is 60°

  11. Protractor Formula C D O Answer is 50°

  12. The Sprinkle of Algebra • Angle Addition Postulate • If angle AOB = 35° • If angle BOC = 20° • What is angle AOC? • 55° B C A O

  13. 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 B C A O

  14. 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

  15. Assignment • Pg 31 -32 • 6 – 23 • 29 & 30

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