1. The problem involves finding the value of angle $x$ in two different triangles based on the given angles. 2. In the first triangle ABC, we know angle $B = 51^\circ$ and angle $A = x^\circ$. Since the sum of angles in any triangle is $180^\circ$, we use the formula: $$A + B + C = 180^\circ$$ 3. Substitute the known values: $$x + 51 + C = 180$$ 4. To find $x$, we need the value of angle $C$. However, it is not given explicitly, so we cannot solve for $x$ directly in the first triangle without additional information. 5. In the second triangle ABC, angle $A = 71^\circ$ and there is a smaller right triangle inside it with one angle $x^\circ$ adjacent to angle $A$. 6. Since the smaller triangle is right-angled, one angle is $90^\circ$. The sum of angles in the smaller triangle is also $180^\circ$: $$x + 71 + 90 = 180$$ 7. Simplify the equation: $$x + 161 = 180$$ 8. Solve for $x$: $$x = 180 - 161 = 19^\circ$$ Therefore, the value of angle $x$ in the second triangle is $19^\circ$. Final answer: $x = 19^\circ$