Non Ecludiean geometry

Let’s walk (and dogsled, and  swim)  from the North Pole along the Greenwich meridian (0 deg. longitude) through England and down to the Equator.  Here make a right turn.  That’s a 90 degree angle.  Go until you hit San Salvador Island, west of Ecuador, located on the Equator at the 90th meridian (+90 degrees) .  Now take another right turn (another 90 degrees) and head back north through St. Louis, back to the North Pole.   So far we’ve taken two right turns, 90+90=180 degrees. But then we hit the North pole again, coming up through Canada.  We find we arrive having completed a triangle.  We took three turns.  But you are coming in at right angles to where we left.   The last angle has 90 degrees.  So we’ve made a triangle containing 90+90+90= 270 degrees, not 180.   Such is life on a curved surface.  Even if you can’t see the curvature while moving around, it is there.