First we find the measurement of dark dot .
ANd for that we have to use the formula of the angle formed by the intersection of chord .
Let the dark dot be t.
So we have
[tex] t =\frac{1}{2} (96+66)=81 [/tex]
t and z are linear pair and sum of angles of linear pair =180 degree.
So we get
[tex] t+z=180
\\
81+z =180
\\
z = 180-81 =99 degree [/tex]
