Question

Need help thaanlksss

Answer 1

Option (3).
`m(\widehat{ACB})=220`

Explanation:

Option (1).

Since measure of an inscribed angle =
`(1)/(2)(\text{measure of the intercepted arc})`

m∠ABC =
`(1)/(2)m(\widehat{AC})`

`m(\widehat{AC})` = 2(m∠ABC)

= 2(30°)

= 60°

Therefore, this option is not true.

Option (2),

Since,
`m(\widehat{AB})+m(\widehat{BC})+m(\widehat{AC})=360`

`m(\widehat{AB})+160+60=360`

m(arc AB) = 360 - 220

= 140°

Therefore, this option is not correct.

Option (3),

`m(\widehat{ACB})=m(\widehat{AC})+m(\widehat{BC})`

= 60° + 160°

= 220°

Option (3) is the correct option.

Option (4),

`m(\widehat{CBA})= 360-m(\widehat{AC})`

= 360° - 60°

= 300°

Therefore, this option is not correct.