At each vertex of the triangle, four angles meet which must add up to 360 °. Therefore altogether the twelve angles add up to 3 x 360 °. Six of the angles are right-angles, and three of them are the internal angles of the triangle, which add up to 180 °.

So the sum of the remaining three angles must be (3 x 360 °) - (6 x 90 °) - 180 ° = 360 °.