Trisected Area 2

Geometry Level 4

Consider a right triangle with the two acute angles satisfying \(\alpha^\circ + \beta^\circ = 90^{\circ}\). How many different ways can we assign the positive values \(\alpha\) and \(\beta\) such that trisecting the right angle yields at least a pair of congruent triangles among the three small triangles ?

Bonus: Generalize this for \(n\)-section, where \(n \geq 2\).