1. Lesson 5-1: Angles and Degree Measure
LEQ - What are co-terminal angles and reference angles?
Lesson 5-1:
Angles and
Degree Measure

2. Angles – two rays joined at a vertex
Angles – two rays joined at a vertex. Angle are measured in degrees, minutes and seconds.
Standard Position – all angles in the coordinate plane have their initial side on the x-axis.

3. Give the angle measurements for each of the following:
Positive angles are measured counter-clockwise
Negative angle are measured clockwise
Give the angle measurements for each of the following:
3 clockwise rotations
2.4 counterclockwise rotations

4. Reference Angle – positive, acute angle formed between terminal side and x-axis.
In your notes, sketch each angle and indicate the reference angle measure:
a.) 150º
b.) -315º
c.) 225º

5. Quadrantal Angles – angles whose terminal side lies on the axes.

6. Coterminal angles – angles which differ by 360º and have the same terminal side.
If αis the degree measure of an angle, then all angles meas°, where k is an integer, are coterminal with α.
Ex. Identify all angles coterminal with 45°

7. Coterminal angles – angles which differ by 360º and have the same terminal side.
If 775º is in standard position, Determine a coterminal angle that is between 0 and 360º. State the quadrant in which the terminal side lies.
If -777º is in standard position, Determine a coterminal angle that is between 0 and 360º. State the quadrant in which the terminal side lies.

8. latitude and longitude lines on earth
Angle conversion Angles are measures in degrees, minutes and second. A minute is 1/60 of a degree and a second is 1/60 of a minute. (ex. 32º 5' 2.34" )
latitude and longitude lines on earth

9. Angle conversion Angles are measures in degrees, minutes and second
Angle conversion Angles are measures in degrees, minutes and second. A minute is 1/60 of a degree and a second is 1/60 of a minute. (ex. 32º 5' 2.34" )
Example: Convert ° to degrees, minutes and seconds.
329° + (0.125  60)
329° + 7’ + (0.5  60)
329° + 7’ + 30”
Example: Convert ° to degrees, minutes and seconds.

10. Angle conversion Angles are measures in degrees, minutes and second
Angle conversion Angles are measures in degrees, minutes and second. A minute is 1/60 of a degree and a second is 1/60 of a minute. (ex. 32º 5' 2.34" )
Example: Convert 39°.5’34” to a decimal, (just degrees).

11. What is the high school’s latitude and longitude?
Convert latitude and longitude to just degrees.

12. Angle Conversion: Convert 52.125º to degrees, minutes and seconds.

13. Graphing calculator: Convert 52.125º to degrees, minutes and seconds.

14. LESSON VOCABULARY REVIEW
Vertex
Initial side
Terminal side
Degrees
Minutes
Seconds
Quadrantial Angle
Co-terminal Angle