Given the triangle is isosceles.
Therefore, the base angles would be equal.
[tex]\begin{gathered} 7x+1=5x+9 \\ 7x-5x=9-1 \\ 2x=8 \\ x=\frac{8}{2}=4 \end{gathered}[/tex]Therefore the base angles are,
[tex]\begin{gathered} 7x+1=7\times4+1=29 \\ 5\times4+9=20+9=29 \end{gathered}[/tex]As the sum of all the interior angles in triangle is 180, we have,
[tex]\begin{gathered} v\text{ertex angle+}29+29=180 \\ \text{vertex angle=180-29-29=}122 \end{gathered}[/tex]Thus, the vertex angle is 122.
