What shape has only obtuse angles?


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Oddman answered
Any regular polygon with more than 4 sides.

Polygons with more than 4 sides don't have to be regular to have all obtuse angles. The number of degrees in an average angle of an n-sided polygon will be
That number will be greater than 90 degrees when
  (n-2)*180/n > 90
  180n - 360 > 90n    (multiply by n)
  90n > 360    (add 360-90n)
  n > 4    (divide by 90)
Any polygon with 5 or more sides can be drawn so that it has all obtuse angles.

Many 3-dimensional shapes have all obtuse angles, a dodecahedron for example.

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