2 Answers

Jeffery Thomas · Answer 1 · 2018-10-30T07:57:53+0000

Answer:

The correct option is C.

Explanation:

According to the central angle theorem, the angle inscribed on the circle is half of its central angle.

$\angle ABC=(\angle AOC)/(2)$

$85=(\angle AOC)/(2)$

$85* 2=\angle AOC$

$170=\angle AOC$

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°.

$\angle AOC+\angle BOC+\angle AOB=360$

$170+64+\angle AOB=360$

$234+\angle AOB=360$

$\angle AOB=360-234$

$\angle AOB=126$

The measure of angle AOB is 126°. Therefore the value of Z is 126 and option C is correct.

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