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:
, and
, and
Thus:
From parallelogram m , so
But via isosoles, , and .
Thus
.
Now, using that is a diameter, get
Thus
.
But from and Side-Angle-Side, get
, and so .