In Euclidean geometry, the sum of the measures of the interior anglesof a pentagon is 540o. Predict how the sum of the measures of the interior angles of a pentagon would be different in spherical geometry.

Answer 1

consider a triangle on a globe
so that one vertex is at the north pole, another on the intersection of the equator and the prime meridian, and the third on the intersection of the equator and the 90° meridian.

Wouldn't the angle at the pole be 90° as well as the two angles on the equator?
Thus the sum of the angles of the triangle would be 270°

Can you set up some kind of similar argument for a pentagon?

Answer 2

In Euclidean geometry, the sum of the measures of the interior angles of a pentagon is 540°. Predict how the sum of the measures of the interior angles of a pentagon would be different in spherical geometry.