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put this solution on YOUR website!A triangle's interior angles add up to 180 degrees. And vertical angles have the same measure as their opposite angles. On the outside triangles all the angles are labeled except for the ones that are vertical angles with that triangle in the middle. Since the three unlabeled angles are vertical angles to angles that add up to 180 they must also add up to 180. If we add up all the angles of those outside triangles we'll get 180+180+180 since there are three of them, but then we need to subtract off the three angles which added up to 180. So we get 180+180+180-180 which would give us 360.
