There is some confusion on your induction.
$n=1$ does not make sense, since polygons have at least 3 sides (a triangle).
This step, although not really wrong, is unnecessary. You are simply renaming $n$ as $k$.
This is ok, might you should be careful when renaming $n=k$ in step 2 (I'm being somewhat pedantic here).
Induction works as follows: take a property $P(n)$ about natural numbers (for example, "$n$ is even", or "The sum of the inner angles of any polygon with $n$ sides is $180^o(n-2)$"), which might be true or false. Fix a number $M$. Then we prove
- $P(M)$ is true.
- If $P(n)$ is true for some $n$, then $P(n+1)$ is true.
And the induction principle says that $P(n)$ is true for all $n\geq M$. In your case you need to show.
- The sum of the angles of any 3-sided polygon (a triangle) is $180^o$.
- Assume that the sum of the angles of any polygon of $n$ sides is $180^o(n-2)$. Then we need to show that the sum of the angles of any polygon of $n+1$ sides is $180^o(n-1)$.
To prove $2$, start with a polygon $P$ of $n+1$ sides. You need somehow to use the hypothesis, that is, make a polygon of $n$ sides appear, and calculate the angles somehow. You should do this by yourself.