I am looking for an aswer to the following construction construct a triangle given two angles (3 angles) and the sum of two sides
Step 1: Draw a line $AB$ of arbitrary length. Copy angle $\alpha$ at point $A$ and angle $\beta$ at point $B$ to form $\triangle ABC$.
Step 2: Extend line $AB$ in the direction of $B$ by length $AC$, calling that line $AD$.
Step 3: Draw line a perpendicular to $AD$ at $A$, and mark off the given required sum of two sides $s$ such that the length of $AE$ is $s$. Connect points $D$ and $E$ to form line $DE$.
Step 4: construct a line parallel to $DE$ passing through point $B$. This line intersects line $AE$ at some point $F$.
Step 5: Copy angle $\alpha$ such that one leg is on $AF$ and the vertex is at $A$. Copy angle $\alpha$ such that one leg is on $AF$ and the vertex is at $A$. Copy angle $\beta$ such that one leg is on $AF$ and the vertex is at $F$. The two new lines meet at some point $G$.
Triangle $AFG$ is the required triangle.
Note that the solution is not unique, unless the problem has specified that the sum of two sides meeting at a specific one of the angles must be the given sum.