Answer
In Euclidean geometry, a basic assumption states that if there is a given line and a point is taken which is not on that given line, only one line can be drawn parallel to the given line and passing through that particular point. This is the assumption that was altered in both hyperbolic as well as elliptic geometries.
Work Step by Step
If there is a point that lies outside a given line, there can possibly be only one line that will pass through that point outside the given line and will be parallel to it at the same time. This is the assumption that proves the angle sum property of a triangle, that is, the sum of angles of a triangle is\[{{180}^{\circ }}\].
But this assumption does not hold true in case of non-Euclidean geometries like hyperbolic geometry and elliptic geometry. In hyperbolic geometry, it is assumed that given a point not on a line, there are an infinite number of lines through the point that does not makes intersection with the given line and elliptic geometry assumes that there no parallel lines.
Because of this alteration in the assumption, the sum of angles of a triangle in hyperbolic and elliptic geometries is either more or less than\[{{180}^{\circ }}\].
