Question

In spherical geometry, which indicates the possible number of right angles a triangle may have?

Answer 1

In planar geometry, we know that the sum of all angles of a triangle is exactly 180°, However, in spherical geometry, different rules apply. When three arcs drawn on the surface of the sphere are connected together through vertices, that is called a spherical triangle. In that case, the sum of all three angles of a spherical triangle is between 180° and 540°.

So, if a triangle has one 90° angle, there are still excess angles to make up for a maximum of 540°. The same is true for two 90° angles. You would exceed 180° but that is just the lower limit so that is still acceptable. If you have three 90° angles, you form a spherical triangle with a total of 270°, which is within the given range. Thus, the answer is all of the above.