First find the angle 1: Here two chords are intersecting. So, the angle 1 formed by two intersecting chords is:
[tex]\begin{gathered} m\angle1=\frac{(105^{\circ}+85^{\circ})}{2} \\ =\frac{190^{\circ}}{2} \\ =95^{\circ} \end{gathered}[/tex]
Now the sum of angle 1 and angle 2 is 180 degrees.
So,
[tex]\begin{gathered} m\angle1+m\angle2=180^{\circ} \\ 95^{\circ}+m\angle2=180^{\circ} \\ m\angle2=180^{\circ}-95^{\circ} \\ m\angle2=85^{\circ} \end{gathered}[/tex]
So, the measure of angle 2 is 85 degrees.
