Question

PLZ HELP ASAP CIRCLES

Answer 1

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°