



 
Joan, Take four points on the equator  that's a quadrilateral with four angles of 180 degrees. If you are not happy with that quadrilateral, you can take the points just above the equator and then have four angles that are nearly 180 degrees. In other words, a quadrilateral can have 4 obtuse angles. (As you point out, any quadrilateral on the sphere must have at least one obtuse angle.) Chris  


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