Answer:
Option (3). [tex]m(\widehat{ACB})=220[/tex]
Step-by-step explanation:
Option (1).
Since measure of an inscribed angle = [tex]\frac{1}{2}(\text{measure of the intercepted arc})[/tex]
m∠ABC = [tex]\frac{1}{2}m(\widehat{AC})[/tex]
[tex]m(\widehat{AC})[/tex] = 2(m∠ABC)
= 2(30°)
= 60°
Therefore, this option is not true.
Option (2),
Since, [tex]m(\widehat{AB})+m(\widehat{BC})+m(\widehat{AC})=360[/tex]
[tex]m(\widehat{AB})+160+60=360[/tex]
m(arc AB) = 360 - 220
= 140°
Therefore, this option is not correct.
Option (3),
[tex]m(\widehat{ACB})=m(\widehat{AC})+m(\widehat{BC})[/tex]
= 60° + 160°
= 220°
Option (3) is the correct option.
Option (4),
[tex]m(\widehat{CBA})= 360-m(\widehat{AC})[/tex]
= 360° - 60°
= 300°
Therefore, this option is not correct.
