It is given that angle 1 and angle 2 are vertical angles.
It is known that the vertical angles are congruent.
Therefore it follows:
[tex]\begin{gathered} m\angle1=m\angle2 \\ 6x+11=10x-9 \\ 11+9=10x-6x \\ 20=4x \\ x=5 \end{gathered}[/tex]
So the value of angle 1 is given by:
[tex]\begin{gathered} \angle1=6x+11 \\ =6\times5+11 \\ =41 \end{gathered}[/tex]
Hence the angle is 41 degrees.
