SOLUTION: for which regular polygon is the ratio of an exterior angle measure to an interior angle measure 1 to 1? 2 to 1? 3 to 1?

Question 1022635: for which regular polygon is the ratio of an exterior angle measure to an interior angle measure 1 to 1? 2 to 1? 3 to 1?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
for which regular polygon is the ratio of an exterior angle measure to an interior angle measure 1 to 1? 2 to 1? 3 to 1?
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1 to 1::
ext + int = 180
ext = int
-----
2ext = 180
ext = 90 degrees
---
# of sides = 360 deg/90 deg = 4 (square)
-------
2 to 1::
ext + int = 180
ext = 2int
-----
ext + (1/2)ext = 180
(3/2)ext = 180
ext = 120 degrees
# of sides = 360 deg/120 deg = 3 (equilateral triangle)
--------------------------
3 to 1
ext = 3int
ext + int = 180
---
4 ext = 180
ext = 45 degrees
----
# of sides = 360 deg/45 deg = 8 sides (octagon)
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Cheers,
Stan H.
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