Question

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

Answer 1

In Euclidean geometry, the angles at the vertices are equal to  540/5 = 108 deg.
In spherical geometry the angles at the verticles are equal to 90+90 = 180 deg

Hence the sum of all interior angles is = 180 * 5 = 900 deg