Is euclidean principle wrong?

Is euclidean principle wrong?I will explain the previous post with an example.Consider, for example, the surface of the Earth.The nearest thing to a straight line on the surface of the Earth, is what is called, a great circle.These are the shortest paths between two points, so they are the roots that air lines use.Consider now the triangle on the surface of the Earth, made up of the equator, the line of 0 degrees longitude through London, and the line of 90 degrees longtitude through Bangladesh. The two lines of longitude, meet the equator at a right angle 90 degrees. The twolines of longitude also meet each other at the north pole, at aright angle, or 90 degrees. Thus one has a triangle with three right angles. The angles of this triangle add up to two hundred and seventy degrees. This is greater than the hundred and eighty degrees, for a triangle on a flat surface. If one drew a triangle on a saddle shaped surface, one would find that the angles added up to less than a hundred and eighty degrees.