PDR,no, using the world, take a plane from the poles along a circle of longitude. The angle between the axis from the centre of the earth to the pole and a line of longitude at the pole is 90. The angle between the axis and a radial to the equator is also 90 which gives 3 internal angles summing to 270.
The issue is not that it is 3-dimensional, it clearly isn't, but that Euclidean geometry, where the internal angles of a triangle sum to 180, is based on straight lines.