No, because the sum of the 3 angles of a triangle always equals 180 degrees. If two angles are supplementary by definition the two together already sum to 180 degrees, leaving no "space" for the third angle.
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It is impossible to have a triangle with 3 right angles. It is possible to draw a triangle with three right angles on the surface of a sphere: www.metacafe.com/watch/769025/270_degree_triangle_yes_3_right_angles
You can draw a triangle with two obtuse angles in a sphere
No because an equilateral triangle has 3 equal acute angles of 60 degrees
Yes providing its other two acute angles are of different sizes
Nope, that is not possible. Equilateral triangles always have three 60 degree angles, which are all acute.