Finding Unknown Angles in Triangles

43) Find $x$ in the first triangle where the base $BC$ contains a point such that the distance from $A$ to that point is equal to the distance from $B$ to that point. $\angle C = 40^\circ$.

44) Find $x$ in the second triangle where $\triangle ABC$ is a right triangle at $B$. $D$ is the midpoint of $AC$. $\angle ADB = 72^\circ$. Determine the value of $x$ ($\angle DBC$).

This question includes visual content: The image contains two geometry problems. Question 43 shows a larger triangle $ABC$. A line segment is drawn from $A$ to the midpoint of the base $BC$. This internal line segment and the segment on the left of the base are marked as equal length. The angle at $C$ is $40^\circ$ and the angle $ABC$ is labeled as $x$. Question 44 shows a right triangle $ABC$ with the right angle at $B$. A line segment $BD$ is drawn to the hypotenuse $AC$. Segment $AD$ and $DC$ are marked as equal in length (making $D$ the midpoint). The angle $ADB$ is given as $72^\circ$. The small angle $DBC$ is labeled as $x$.