Question

Need help thaanlksss

Answer 1

Answer:

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

Step-by-step explanation:

Option (1).

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

m∠ABC = $\frac{1}{2}m(\widehat{AC})$

$m(\widehat{AC})$ = 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.