One complete counterclockwise rotation measures 360° and one complete clockwise rotation measures −360°. Thus, 1° is equal to 1/360 rotation (counterclockwise) and 90° is equal to 90/360 or 1/4 rotation (counterclockwise). To find the angle measure in degrees for a given rotation, multiply the amount of rotation by 360° for counterclockwise rotation or by −360° for clockwise rotation.

1. ANGLE
MEASURES
Lesson 1

2. Angle Measures in Degrees
• One complete counterclockwise rotation measures 360° and one
complete clockwise rotation measures −360°.
• Thus, 1° is equal to
1
360
rotation (counterclockwise) and 90° is
equal to
90
360
or
1
4
rotation (counterclockwise).
• To find the angle measure in degrees for a given rotation,
multiply the amount of rotation by 360° for counterclockwise
rotation or by −360° for clockwise rotation.

3. Example: Finding the degree measures of angles for given rotation.

4. Try this.
Find the degree measure for each given rotation.
a.
7
6
rotations; clockwise
b.
3
5
rotations; counterclockwise

5. Kinds of Angles
Angles are also named based on the size or amount of rotation
made by the terminal side of the angle.

6. Kinds of Angles

7. Kinds of Angles

8. Converting Degrees, Minutes, and Seconds to Decimal Degrees,
and Vice Versa
• The degree is also divided into minutes and seconds and
measurements in degrees can also be written in decimal form.

9. Example:
Converting degrees, minutes, and seconds to decimal degrees
Try this.
a. Convert 30°15′ to decimal degrees.
b. Convert 251°30′18" to decimal degrees.
Do this.
a. Convert 94°46′ to decimal degrees.
b. Convert 38°42′18" to decimal degrees.

10. Example:
Converting decimal degrees to degrees, minutes, and seconds
Try this.
a. Convert 152.3° to degrees, minutes, and seconds.
b. Convert 68.345° to degrees, minutes, and seconds.
Do this.
a. Convert 53.76° to degrees, minutes, and seconds.
b. Convert 163.624° to degrees, minutes, and seconds.