SK,SN,and SL are radii and therefore equal. The two triangles are congruent. Congruent chords imply congruent arcs
It's all about the angles.
Repeated use of isosoles triangles gives:
From parallelogram m , so
But via isosoles, , and .
Now, using that is a diameter, get
But from and Side-Angle-Side, get
, and so .