we could look at the picture with a bit less lines, check the picture below.
that simply means that those two blue angles are linear angles and therefore add up to 180°.
[tex]\bf (x^2-6x+83)+(106)=180\implies x^2-6x+189=180 \\\\\\ x^2-6x+9=0~~~~ \begin{cases} (-3)(-3)=\stackrel{constant}{9}\\[0.8em] -3-3=\stackrel{\stackrel{\textit{middle~term}}{coefficient}}{-6} \end{cases}\implies (x-3)(x-3)=0 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill x=3~\hfill[/tex]
