so we have a pentagon, namely a polygon with PENTA, 5 sides
[tex]\stackrel{\textit{sum of all interior angles in a polygon}}{T=180(n-2)~\hfill n=sides}~\hfill \stackrel{\textit{since this one has 5 sidses}}{T=180(5-2)\implies T=540} \\\\[-0.35em] ~\dotfill\\\\ (7x-12)+(4x)+(4x+2)+(5x)+(2x)=540 \\\\\\ 22x-10=540\implies 22x=550\implies x=\cfrac{550}{22}\implies x=25[/tex]
Check the picture below.
