The measure of the indicated angle inscribed in the circle is 82 degrees.
The inscribed angle theorem states that "an angle x inscribed in a circle is half of the central angle 2x that subtends the same arc on the circle.
Internal angle = 1/2 × ( major arc + minor arc )
From the diagram:
Major arc BC = 85 degrees
Minor arc DU = 79 degrees
Internal angle =?
To determine the measure of the indicated angle, plug the given values into the above formula and simplify:
Internal angle = 1/2 × ( major arc + minor arc )
Internal angle = 1/2 × ( 85 + 79 )
Internal angle = 1/2 × ( 164 )
Internal angle = 82 degrees
Therefore, the indicated angle measures 82 degrees.