Since the degree of $f(z)$ is two, the highest power of $z$ in $f(z)$ is $z^2$.
Since the degree of $g(z)$ is less than the degree of $f(z)$, the highest power of $z$ in $g(z)$ is less than $z^2$.
Therefore, the highest power of $z$ in $f(z)+g(z)$ is $z^2$.
Therefore, the degree of $f(z)+g(z)$ is $\boxed{2}$.
The answer is: 2
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Suppose $f(z)$ and $g(z)$ are polynomials in $z$, and the degree of $g(z)$ is less than the degree of $f(z)$.  If the degree of $f(z)$ is two, what is the degree of $f(z)+g(z)$?

### Answer:
