Question

the measure of ∠dug m∠dug = ° is given can be calculated cannot be calculated

Explanation:

Step1: Analyze the given information

We are only given an angle of \(90^{\circ}\) at point \(U\), but there is no information about the relationship between \(\angle DUG\) and the \(90^{\circ}\) angle (such as if they are complementary, supplementary, or part of some geometric figure with known angle - side relationships).

Step2: Determine if calculation is possible

Since there is no geometric rule (like vertical angles, adjacent - angle sum in a straight line, or angle - sum in a triangle etc.) that can be applied with the given single \(90^{\circ}\) angle to find \(\angle DUG\).

Answer:

\(m\angle DUG=\text{cannot be calculated}\)