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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 °.
Outside the Boxes
Age 11 to 14
ShortChallenge Level 
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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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