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PBA- let me give you an example of non-Euclidean geometry. Everybody knows a triangle has 180 degrees. Right?
NO! False! That only works on planes not spheres.
For example, assuming the Earth is a perfect sphere, draw a line from the center of the north pole to the equator. That line now forms a 90 degree angle with the equator. Now draw another line from the center of the north pole to the equator, but at a 90 degree angle to the first line. This line is also at a 90 degree angle with the equator. Now connect the 2 lines with another line drawn on the equator.
As you can see, there are three 90 degree angles in this triangle. And 3*90 is 270 degrees; way above 180.