Question 1018762: What is the angle of rotation of this regular octagon? What is the measure of an interior angle?
A.
45°, 135°
B.
22.5°, 135°
C.
45°, 108°
D.
22.5°, 108°
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! octagon interior angle can be calculated as 180 * (n-2) / n.
n = 8.
interior angle = 180 * 6 / 8 = 180 * 3 / 4 = 45 * 3 = 135 degrees.
the internal angle is the supplement of the exterior angle.
the extreior angle is equal to 360 / 8 = 45 degrees.
180 - 45 = 135 degrees.
the angle of rotation is the smallest angle the figure can be rotated and still look the same.
this appears to be 45 degrees.
in fact, it appears that the angle of rotation is the central angle of a regular polygon.
the formula is equal to 360 / n, where n is the number of sides.
here's a reference that discusses exactly the topic you are asking about.
if even shows an octagon as one of the examples.
http://www.emathematics.net/transformations.php?def=rotational
this, in fact, is also the formula for the exterior angle of a polygon.
interior angle = 180 * (n-2) / n
interior angle = 180 - exterior angle.
exterior angle = 360 / n
central angle = 360 / n
it appears that angle of rotation is also equal to 360 / n as well.
your solution should be selection A.
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