7. (40 points) In the convex quadrilateral $ABCD$, $\angle ABD$ $=16^{\circ}, \angle DBC=48^{\circ}, \angle BCA=58^{\circ}, \angle ACD=$ $30^{\circ}$. Find the measure of $\angle ADB$.
7. It is known that $\angle B D C=44^{\circ}, \angle B A C=58^{\circ}$.
Therefore, $B A=B C$.
As shown in Figure 15, let $E$ be a point on side
$C D$ such that
$\angle E B C=4^{\circ}$.
Then $B E=B C=B A$.
Also, $\angle A B E=60^{\circ}$, so

$\triangle A B E$ is an equilateral
triangle.
Since $\angle D B E=44^{\circ}$, it follows that $E D=E B=E A$.
Noting that $\angle D E A=32^{\circ}$, we have
$\angle E A D=\angle E D A=74^{\circ}$.
From this, we can conclude that $\angle A D B=30^{\circ}$.