To create a rectangle like that, where angle B is 60°, I'd do like this.
Create a circle with 3 vertices. This will create an equiangular triangle.
Tab into Edit mode, select one edge and subdivide it once.
Create an edge. Select the middle vertex of the edge you subdivided and the vertex to which it's not connected and hit F.
Delete half of it. Select one of the corner vertices of the edge you subdivided and hit X > V.
Select the other corner vertex of the edge you subdivided and snap cursor to selected (ShiftS > U). Set pivot point to 3D Cursor (see red marking in the image). Select all (A twice), duplicate but cancel the translation (ShiftD > Esc) and rotate 180° around the Z1 axis (RZ180).
Select all (A twice). Duplicate but cancel the translation (ShiftD > Esc) and rotate 180° around the X1 axis (RX180).
Select all (A twice). Remove doubles (CtrlV > D). Select the diagonal you don't want (two edges, three vertices) and delete it (X > E).
Select two adjacent, unconnected vertices and make an edge between thenthem (F), then do the same with the other two adjacent, unconnected vertices.
1I'm in top view. If you're in another view, you will need to rotate around other axes.