This was excluded by the Greeks because their idea of angle required it to be less than a straight angle.
That there exists a triangle, the sum of whose angles is congruent to a straight angle, the Euclidean; II.
That there exists a triangle the sum of whose angles is greater than a straight angle, the Cayley-Klein.
The elliptic or Cayley-Klein hypothesis assumes that the angular sum is greater than a straight angle.