Answer:
The correct option is C.
Step-by-step explanation:
According to the central angle theorem, the angle inscribed on the circle is half of its central angle.
[tex]\angle ABC=\frac{\angle AOC}{2}[/tex]
[tex]85=\frac{\angle AOC}{2}[/tex]
[tex]85\times 2=\angle AOC[/tex]
[tex]170=\angle AOC[/tex]
The measure of angle AOC is 170°.
The length of arc BC is 64°, so ∠BOC=64°.
The sum of all central angle is 360°.
[tex]\angle AOC+\angle BOC+\angle AOB=360[/tex]
[tex]170+64+\angle AOB=360[/tex]
[tex]234+\angle AOB=360[/tex]
[tex]\angle AOB=360-234[/tex]
[tex]\angle AOB=126[/tex]
The measure of angle AOB is 126°. Therefore the value of Z is 126 and option C is correct.
