only one because the angles of the triangle must add up to 180 degrees. if you already know the measurements of the first two, you add them together and subtract that from 180 to find the third angle. therefore, there the answer is one.
The triangle mentioned is an isosceles right triangle: You can draw an infinity of such triangles which all will be similar. Proof: Draw any isosceles right triangle and from any point of 2 equal side draw a parallel (or several parallels ) to the hypotenuse: all resulting triangles will be isosceles right triangle and all will be similar
