3. (10 points) Suppose the lateral area of a certain cone is $10 \pi$, and the total surface area is $19 \pi$, then the central angle of its lateral development is
【Analysis】According to the characteristics of a circular cone, the side of a circular cone is a curved surface, and when unfolded, it is a sector. The base is a circle. The surface area of a circular cone = lateral area + base area. From the problem, we know the base area is $9 \pi$, so the base radius is 3, and the circumference, which is also the arc length of the lateral side, is $6 \pi$.

Let the angle be $A$ and the lateral radius be $R$, then we have $\frac{\mathrm{A}}{360} \times \pi R^{2}=10 \pi, \frac{\mathrm{A}}{360} \times 2 \pi R=6 \pi$, solve accordingly.
【Solution】Solution: Let the angle be $A$ and the lateral radius be $R$, then we have $\frac{\mathrm{A}}{360} \times \pi R^{2}=10 \pi, \frac{\mathrm{A}}{360} \times 2 \pi R=6 \pi$, solving yields: $A=324$ degrees.

Answer: The central angle of its lateral development is 324 degrees. Therefore, the answer is: 324 degrees.