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Outside the Boxes

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

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°.

This problem is taken from the UKMT Mathematical Challenges.