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
So the sum of the remaining three angles must be (3 x
360°) - (6 x 90°) - 180° =
This problem is taken from the UKMT Mathematical Challenges.