The given figure represents a quadrilateral. The sum of the interior angles of a quadrilateral is equal to 360°. This is our working concept to solve for the value of x on the given figure. All we need to do is, to sum up, all the interior angles on the problem and their sum are equal to 360 °. This is written in an equation as
[tex](3x-6)+(x+10)+(2x-8)+x=360[/tex]
Simplify the equation and compute, we get
[tex]\begin{gathered} 7x-4=360 \\ 7x=360+4 \\ \frac{7x}{7}=\frac{364}{7} \\ x=52 \end{gathered}[/tex]
Hence, the value of x on the problem is 52 degrees.
