Answer:
75°
Step-by-step explanation:
∠ESK is the supplement of ∠EDK, so is 100°. ∠ESD = 1/2·arc ED, so is 25°. Since ...
∠ESK = ∠ESD + ∠DSK
you have ...
100° = 25° + ∠DSK . . . . fill in known values
75° = ∠DSK . . . . . . . . . . subtract 25°
_____
Regarding opposite angles of an inscribed quadrilateral
Chord EK divides the 360° circle into two arc: major arc EDK and minor arc ESK. The sum of those arcs is 360°. Each of the inscribed angles that intercepts those arcs has half the measure of the arc. That is, ∠ESK intercepts arc EDK, so has half its measure. Likewise, ∠EDK intercepts arc ESK, so has half its measure. The sum of those opposite angles will be the sum of half the measures of the arcs, so half the sum of the arcs, or 1/2·360° = 180°.
This is why we can say ∠ESK is the supplement of ∠EDK.
