DirectX is using Left handed co- ordinate system, so Can we say DirectX Using only left angle triangles?, or is there any other reasons for that, or it is using both (left angle and right angle) angle triangles?.
What do you mean by left angle triangle? A right-angled triangle (or just right triangle) is a triangle with one right angle (90 degrees). But left angle triangle? There's nothing like that ;)
DirectX is "using" left-handed coordinate system. But this in fact doesn't mean much, you can use right-handed system in DirectX with absolutely no problem if you want. The D3DX library even provided you both LH and RH versions of all functions that are dependent on the coordinate system, like D3DXMatrixPerspectiveRH/LH, D3DXMatrixLookAtRH/LH etc.
Switching between LH and RH system requires just proper view and projection matrices (using the above mentioned functions with proper ending ...RH / ...LH), proper winding order of your triangles vertices (+ proper backface culling mode) and maybe proper layout of cube textures? None of these is strictly dictated by DirectX, it depends purely on you - on how do you generate your meshes (in 3ds max or maya or ...) and how do you set the transform matrices.
Btw, of course also your world/scene/map/terrain/whatever coordinates must correspond to the coordinate system you're using, but this has ABSOLUTELY nothing to do with DirectX.