Question

measures
the measure of \\( \angle d u g \\) can be calculated.
\\( m \angle d u g = \\) 。

Explanation:

Step1: Use the property of vertically - opposite angles

Vertically - opposite angles are equal. The angle adjacent to the \(40^{\circ}\) angle (vertically - opposite to it) is \(40^{\circ}\).

Step2: Use the angle - subtraction formula

We know that the large angle (which is \(90^{\circ}\)) and \(\angle DUG\) are related. Let the measure of \(\angle DUG\) be \(x\).
We use the formula \(x = 90^{\circ}-40^{\circ}\)

Answer:

\(50\)