The three angles of a triangle add up to 180 in Euclidean space (that is, a "flat" triangle, not one drawn on a curved surface). If two angles already add up to 180 the third angle must be zero. If the triangle is drawn on a sphere it is possible for the triangle to have 3 angles of 90 degrees each, such as a triangle drawn with a right angle at a pole The figure ceases to be a triangle.
For example, two right angles in one "flat" triangle add up to 180. The two sides would be parallel so would never meet. If one angle of a triangle was 60 degrees and the other 120, again two sides would be parallel, because the external angle would be 120 or 60.
Two angles of a "flat" triangle cannot both be 180 degrees. The "triangle" would simply be a straight line. But lines drawn round a sphere form a spherical triangle. As two curved sides of the triangle approach a semi-circle the angle between them approaches 180 degrees.
A spherical triangle's sides are formed by the intersection of three great circles, so a spherical triangle can, for example, contain three right angles. So the sum of the angles in this case would be 270 degrees. Great circles have equal circumferences=2(pi)r where r is the radius of the sphere. All great circles have the same centre. The shortest distance between two points on a sphere is on the circumference of the great circle that passes through both of them.
