Question 16
The size of the angle $ABC$, expressed in degrees, in a right triangle $ABC$ is an integer. It is known that for some positive integer $n$, one can choose points $K_0 = A$, $K_2, \dots, K_{2n}$ on the hypotenuse $AB$ and points $K_1 = C$, $K_3, \dots, K_{2n+1} = B$ on the leg $CB$ in such a way that each triangle $K_{i-1}K_iK_{i+1}$ with $i = 1, \dots, 2n$ is isosceles with base $K_{i-1}K_{i+1}$. Find all possible values of the size of angle $ABC$.