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 $n \geq 2$ .

Inspiration