1. **State the problem:** We are given a circle with points A, B, C, and D on its circumference. Triangle ABD has an angle at vertex A of 56° and triangle BCD has an angle at vertex C labeled as $g$. We need to find the value of $g$. 2. **Recall the property of cyclic quadrilaterals:** Since A, B, C, and D lie on the circle, quadrilateral ABCD is cyclic. Opposite angles of a cyclic quadrilateral sum to 180°. 3. **Identify opposite angles:** Angle $A$ and angle $C$ are opposite angles in the cyclic quadrilateral ABCD. 4. **Apply the cyclic quadrilateral angle sum property:** $$ \angle A + \angle C = 180^\circ $$ Substitute the known value: $$ 56^\circ + g = 180^\circ $$ 5. **Solve for $g$:** $$ g = 180^\circ - 56^\circ = 124^\circ $$ **Final answer:** $$ g = 124^\circ $$