An inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords. Using the following formula

We have that

We have the measure of the angle ∠ADB, which is 43º. The arc AB is:

∠AOB is a central angle, therefore, the measure of the intercepted arc(which is AB) is equal to the measure of ∠AOB.

The measure of ∠AOB is equal to the measure of m∠BOC, therefore

The angles ∠AOB and ∠BOC together create the central angle ∠AOC, that intercepts the arc AC, therefore

The arc AC is also intercepted by the chords that form the angle ∠ADC, therefore

The angle ∠ADC is formed by the sum of the angles ∠ADB and ∠BDC, therefore, we have

The measure of the angle ∠BDC is 43º.