The whole point of tessellation is that infinitely many copies of the shape can be used to cover an infinite plane surface without gaps or overlap. So, obviously, the answer is infinitely many times!
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A triangle can have at most one obtuse angle, but triangles do not necessarily have any obtuse angles.
An obtuse triangle is a triangle that has one angle greater than 90 degrees.
There are infinitely many. For example, every different triangle can tessellate. There are 15 types of pentagons which will tessellate.
No right triangle can have any obtuse angles inside it.
An obtuse triangle can have no right angles, and has two equal angles.