Question

the measure of \\( \angle gax \\) can be calculated. \\( m \angle gax = \\) 。

Explanation:

Step1: Use the angle - bisector property

Since \(AD\) is the angle - bisector of \(\angle GAX\), if we assume the measure of \(\angle GAX = 2x\). But we can also use the fact that the angle between two lines and the bisector. Another approach is to note that if we consider the construction of the angle bisector. The measure of \(\angle GAX\) is \(110^{\circ}-90^{\circ}= 20^{\circ}\) (assuming the arcs and the construction of the angle bisector. The difference between the two arcs' measures gives the angle we want. If we consider the full - circle or semi - circle concepts, but in terms of the basic angle subtraction for the constructed angle.

Answer:

\(55\)