First, find the missing angle of the triangle. Remember that the internal angles of a triangle should add up to 180°, then, the missing angle is given by:
[tex]180-64-27=89[/tex]On the other hand, the angle of 89° plus the angle of (97+x)° should add up to 180 since they are adjacent angles on a straight line. Then:
[tex]89+(97+x)=180[/tex]Solve for x:
[tex]\begin{gathered} \Rightarrow89+97+x=180 \\ \Rightarrow186+x=180 \\ \Rightarrow x=180-186 \\ \Rightarrow x=-6 \end{gathered}[/tex]Therefore, the value of x is:
[tex]-6[/tex]