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The ancient Greeks used base 6 numbers and thought that the number 6 had some kind of power. This thinking was backed up by the number of days in a year. When the Ancients went about measuring the year, they watched the sun set each day over the horizon. Where it set, it would be marked on a circle. After a while, they noticed that about 360 of these evenly spaced marks would fill up a circle. Any rounding error is because of the power of the number 6 and 6*6=36 and so this was special too and the number of degrees of a circle became 360. 360/24=15degrees => the earth turns 15 degrees in an hour 60 seconds a minute, 60 minutes an hour => 3600 seconds and hour This is also why angles are measure by degrees (o), minutes ('), and seconds ("). 360 degrees is an arbitrary number that (roughly) matches the length of the year by chance. Gradients are another measurement of angle defined as there being 100 (an arbitrary number based on our number system) Gradients in a circle. A better mathematical measurement of angles is radians. There are pi~3.141 radians in a circle.

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Q: Why do we use 360 when measuring angles?
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What is the instrument use in measuring angles?

a protractor


What is a polygon with all the interior angles measuring 900?

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A polygon has interior angle 165 degrees how many sides has it?

A regular polygon with interior angles measuring 165 degrees each will have exterior angles measuring 15 degrees each, since each pair of interior/exterior angles forms a linear pair whose measures total 180 degrees. For any polygon, the sum of the exterior angles is 360 degrees. You can find how many sides, and therefore vertices, in the polygon by dividing 360 by 15. In this case, the polygon has 360/15 = 24 sides.


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A protractor is the most accurate way of measuring angles.


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