All triangles have 3 sides and therefore 3 corners - this means there are 6 usefully measurable angles - 3 internal and 3 external.
In theory you could make an infinite number of measurements along a side, but in each case the angle would be 180 degrees as it is a straight line.
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one
Just the one.
Just the one and the other two angles must then be acute angles
If its a triangle then just the one but if it is a square or a rectangle then 4 of them.
There is no such shape since an angle can always be added to any shape.