Lesson Worksheet: Angles in Degrees, Minutes, and Seconds Mathematics

In this worksheet, we will practice converting the measure of angles from degrees, minutes, and seconds to only degrees and vice versa.


How can you write 20 degrees, 25 minutes, and 59 seconds?

  • A252520
  • B255920
  • C202559
  • D592520


Using a calculator, write 253045 in degrees.


Convert the angle 461520 to decimal degrees giving the answer to three decimal places.


Express the angle 52.113611 in degrees, minutes, and seconds.

  • A52649
  • B524949
  • C5266
  • D52496


Using a calculator, write 18.15 in degrees, minutes, and seconds.

  • A191112
  • B161523
  • C171210
  • D1890
  • E201035


Without using a calculator, write 203045 in degrees.


Without using a calculator, write 20.7 in degrees, minutes, and seconds.

  • A21435
  • B20420
  • C23452
  • D22441
  • E24463


Michael is trying to convert 814735 to degrees only without using a calculator. First, he converts the minutes to degrees by dividing 47 by 60, and then he converts the seconds to minutes by dividing 35 by 60. Finally, he adds all of the parts of the degree to get his answer. His answer is 82.3667.

Is his process correct?

  • ANo
  • BYes

If you think that his process is wrong, which of the following is correct?

  • AI think his process is correct.
  • BHe should add all of the degrees, minutes, and seconds by dividing the minutes or seconds by 60. So, his answer will be 163.
  • CHe should divide the 35 seconds by 60 times 60(3,600) to convert it to degrees. So, his answer will be 81.793.


Noah’s teacher asked him to express 585940 in degrees only without using the calculator. Noah forgot the procedure, so he could not answer his teacher’s question. His teacher requested that his colleagues, Liam, Anthony, and Jacob, help him. Liam said the answer was 157, Anthony said the answer was 58.9944, and Jacob said the answer was 59.65. Whose answer is correct?

  • ALiam
  • BAnthony
  • CJacob


Liam and Matthew are using their calculators to convert 77.1259 to degrees, minutes, and seconds. Liam says the answer is 77733.24. However, Matthew says the answer is 761233. Using your calculator, determine which answer is correct.

  • AMatthew
  • BLiam

This lesson includes 17 additional questions and 198 additional question variations for subscribers.

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