Answer:
x=0
Step-by-step explanation:
Given circle O such that:
[tex]mAB=120^\circ\\m\angle BCA =(x+60^\circ)[/tex]
The measure of arc AB is the measure of [tex]\angle AOB[/tex] which is an angle subtended by arc AB and passes through the center of the circle.
[tex]\angle BCA[/tex] is an angle subtended by arc AB and passes through the the point C on the circle.
By the Inscribed Angle Theorem
[tex]mAB=2 X m\angle BCA \\120^\circ=2(x+60^\circ)\\120^\circ=2x+120^\circ\\2x=120^\circ-120^\circ\\2x=0\\x=0[/tex]
