Explanation:
your picture is asking for something else (but it needs the circumference too).
the full circumference (360°) is
2×pi×r = 2×pi×10 = 62.83185307... in ≈ 62.83 in
and now to the picture question :
the ratio of arc length to the full circumference is the same as the ratio of the arc angle to the full 360°.
8.73/62.83185307... = arc angle DE/360
so,
arc angle DE = 360×8.73/62.83185307... =
= 50.01921551...° ≈ 50.02°