In the adjoining figure, $$ABCDEFGH$$ is a regular octagon. The measure of $$\angle ADG$$ in degrees is ______.

The vertices of a regular octagon lie on a circle, and each central angle is $$\frac{360^\circ}{8}=45^\circ$$. The minor arc from $$A$$ to $$G$$ through $$H$$ spans two sides, so its measure is $$90^\circ$$. The inscribed angle $$\angle ADG$$ subtending this arc is half of $$90^\circ$$, which is $$45^\circ$$.