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Angle evaluating (Posted on 2014-10-28) Difficulty: 2 of 5
You are given a drawing of a certain angle (two intersecting straight lines). How can you evaluate its value (within 2o), using a compass only?

No Solution Yet Submitted by Ady TZIDON    
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Solution One inefficient way. Comment 1 of 1
Without a straightedge this seems a bit tricky, but to be within 2 we need to know what multiple of 4 it is closest to.  

Two things you can do with just a compass is to add the angle to any other angle and to halve and angle.  So add the angle to itself 22 and a half times times, count how many times this goes around and see which quadrantal you are closest to.

For example if given an (unknown) 27.4 angle, adding it to itself 22.5  times takes it to 616.5
Divide by 360 to see this is 1.7125 which to the nearest quarter is 1.75 revolutions = 630
630/22.5 = 28 which is within 2 degrees.

Actually you can just look at the number of revolutions (to the nearest quarter) and multiply by 16.

  Posted by Jer on 2014-10-28 13:56:37
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