 # Angle and Degree Measurement ## What you'll learn

• How angle is defined?
• Basics abouts angles: vertex, positive angles, negative angles
• Degree measurement of an angle
• How degree is defined?
• Subdivision of a degree: minutes, seconds
• Decimal degree and Sexagesimal degree (Degree-minute-second notation or DMS notation of degree)
• Conversion from DMS notation to Decimal degrees
• Conversion from Decimal degrees to DMS notation
• Explanation of 12 Questions ## You're Enrolled!

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Concepts
Definition of an angle
5 min 30 sec
Degree measurement of an angle
5 min 30 sec
Questions
Questions
12 subtopics
Question – 1 : Find the degree measure of the angle for each given rotation
a. \displaystyle {\frac{3}{4}} rotation, counterclockwise
b. \displaystyle {\frac{1}{2}} rotation, clockwise
c. \displaystyle {2\frac{1}{3}} rotation, counterclockwise
d. \displaystyle {\frac{7}{6}} rotation, clockwise
5 min 30 sec
Question – 2 : The earth completes one rotation on its axis every 24 hours. Through how many degrees does a point on the earth rotate in
a. 8 hours
b. 7 days
5 min 30 sec
Question – 3 : Express each angle measure in decimal degrees.
a. \displaystyle{ 40{}^\circ 17’45”}
b. \displaystyle{ 129{}^\circ 10’37”}
c. \displaystyle{ -5{}^\circ 10’24”}
d. \displaystyle{ -48{}^\circ 15”}
Question – 4 : Express each angle measure in degrees-minutes-seconds.
a. \displaystyle{ 13.49{}^\circ }
b. \displaystyle{ 52.66{}^\circ }
c. \displaystyle{ 50.525{}^\circ }
d. \displaystyle{ -10.33{}^\circ}
Question – 5 : A compact disc rotates at a speed of 500 revolutions per minute. Through how many degrees does it rotate to play a song that lasts 2.05 min?
Question – 6 : A large gear rotates at a rate of 3 rotations per minute. Through how many degrees does it rotate in 5 min? In 40 s?
5 min 30 sec
Question – 7 : Some single songs are recorded on one side of records that rotate at a rate of 45 rpm. Through how many degrees does one of these records rotate in 20 s?
5 min 30 sec
Question – 8 : Through how many degrees does the second hand of a clock rotate in 2 h 23 min 20 s?
5 min 30 sec
Question – 9 : Find the measure in decimal degrees of the angle supplementary to 99°12’20”.
5 min 30 sec
Question – 10 : Find the measure in decimal degrees of the angle complementary to 16°5’56”.
5 min 30 sec
Question – 11 : Find the measure in degrees-minutes-seconds of an angle that is \displaystyle{ 11{}^\circ 5’40”} greater than its complement.
5 min 30 sec
Question – 12 : What is the measure in degrees of the smaller of the angles formed by the hands of a clock at 6:12′?
5 min 30 sec
Quizzes
Practice Quizzes
1 quiz
Quiz – 1