Not in traditional, 2 dimensional, euclidean geometry, because a triangles angles always equal 180º .
However, there is a branch of Geometry that deals with a coordinate system on a sphere, instead of a plane, and in spherical geometry a triangle with three right angles is very much possible. Consider, for example, the triangle bounded by the Prime Meridian, 90o west longitude, and the equator.
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A triangle can never have three right angles
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
If one of the angles is 90 degrees then it is right ange triangle If one of the angles is obtuse then it is an obtuse triangle If the three angles are 3 different acute then it is a scalene triangle If two of the angles are equal then it is an isosceles triangle If the three angles are equal then it is an equilateral triangle
Every triangle has three interior angles which total 180 degrees. A right triangle has one of the angles as 90 degrees.
If one of the three interior angles is 90 degrees then it is a right triangle.