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There are a number of theories: the ancient Babylonians counted in the sexagesimal system (counting in 60s). This was extended to 6*60 = 360, a number which was close to the number of days in the year. Also, 360 is divisible by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20 etc which is convenient.
In any case, pure mathematicians do not measure angles in degrees - they use radians.
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What is the measure of the exterior angles of a pentagon?
The sum of the exterior angles of any polygon must be 360 degrees. Subject to that constraint, individual angles can have any measure between 0 and 360 degrees.
What is the total angle measure of a nonagon?
Exterior angles 360 degrees Interior angles 1260 degrees
What polygon has angle measure that add up to 360 degrees?
The exterior angles of every polygon sum to 360 degrees. The interior angles of every quadrilateral sum to 360 degrees.
Total measure of exterior angles of a heptagon?
360 degrees
What is the sum of the measure of the angles of a decagon?
Interior angles add up to 1440 degrees Exterior angles add up to 360 degrees
