From the figure we are given that the measure of angle U is equal to 85°. With this, we can conclude that the arc intercepted by the angle which is the arc DKC will have a measure that is twice its value.
m(DKC) = 2(85°) = 170°
The total measure of the arc in a circle is equal to 360°. Hence,
m(DKC) + m(DUC) = 360°
Substituting the known value,
170° + m(DUC) = 360°
The value of m(DUC) is equal to 190°. The measure of the angle K is half this value.
m∠K = 190°/2 = 95°
Answer: 95°