Estimating Angles

A complete circle has 360°.  We often hear commentators saying things like “Nice 360!” or “He did a total 180°”.  Well this is Math talk.  If I were to turn in a circle, I would have rotated 360°.  If I turned around and faced where my back was a moment ago (half a circle), I would have turned 180°.

circle anglesWhen estimating a degree it is important to use a benchmark (a point of reference) when making an estimate.  Lets take a look at this picture.  We can see that in this case, we are starting from the top and moving clockwise around the circle.  This particular circle has been cut into eight pieces.  By learning and remember this circle, we can estimate angles much more accurately.

Look at this angle:

45 blank

You can look at this angle, and using the knowledge we know from learning the picture on the left, we can see that this angle is about the size of one piece of the puzzle. Since it is about the size of one piece of the puzzle, it should measure around 45°.  Lets check it out!

45 degree angle

We can see that the angle does in fact measure 45°.  Using this concept, we can estimate more difficult angles as well!  Lets try!

unknown angle 1

Using what we know from the eight piece circle, we can look at this angle.  Does it look bigger than a single piece?  I would say so!  Is it a s big as two?  No?  Than we know  that this angle is going to be between 45° and 90°.  (Each piece measure 45°.  °+ 45° =90)

So the new range for this angle become between 45° and 90°.  Is 100° between 45° and 90°? No!  Therefore 100° is not a reasonable estimate. What about 40°?  Too small!  40°is smaller than 45°.  If I said 75° or 80°, would that be reasonable? Yes.  Either of those would be a reasonable estimate for this angle.


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