Paper 3, Section I, E

Geometry
Part IB, 2019

State a formula for the area of a spherical triangle with angles α,β,γ\alpha, \beta, \gamma.

Let n3n \geqslant 3. What is the area of a convex spherical nn-gon with interior angles α1,,αn\alpha_{1}, \ldots, \alpha_{n} ? Justify your answer.

Find the range of possible values for the interior angle of a regular convex spherical nggnn-g \mathrm{gn}