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.

A.
The sum would be greater than 540°.
B.
The sum would still be 540°.
C.
The sum would be less than 540°.
D.
The sum would less than or greater than, but never equal to, 540°.

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.




A.
The sum would be greater than 540°.
B.
The sum would still be 540°.
C.
The sum would be less than 540°.
D.
The sum would less than or greater than, but never equal to, 540°.

zpupster · Answer

Think of a pentagon drawn on the plane. Now as you stretch the figure to wrap around a sphere, the angles spread apart, getting bigger