The sum of the interior angles of a quadrilateral is 360. So, we have
[tex]\hat{R}+\hat{S}+\hat{T}+\hat{U}=360[/tex]
Since [tex]\hat{R}=\hat{T}[/tex] and [tex]\hat{U}=\hat{S}[/tex], the formula becomes
[tex]2\hat{R}+2\hat{S}=360[/tex]
which simplifies to
[tex]\hat{R}+\hat{S}=180[/tex]
Substitute the expressions for R and S:
[tex](6x-4)+(2x+8)=8x+4=180 \iff 8x=176 \iff x=22[/tex]
