Answer:
Option (3). ![m(\widehat{ACB})=220](https://tex.z-dn.net/?f=m%28%5Cwidehat%7BACB%7D%29%3D220)
Step-by-step explanation:
Option (1).
Since measure of an inscribed angle = ![\frac{1}{2}(\text{measure of the intercepted arc})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28%5Ctext%7Bmeasure%20of%20the%20intercepted%20arc%7D%29)
m∠ABC = ![\frac{1}{2}m(\widehat{AC})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dm%28%5Cwidehat%7BAC%7D%29)
= 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](https://tex.z-dn.net/?f=m%28%5Cwidehat%7BAB%7D%29%2Bm%28%5Cwidehat%7BBC%7D%29%2Bm%28%5Cwidehat%7BAC%7D%29%3D360)
![m(\widehat{AB})+160+60=360](https://tex.z-dn.net/?f=m%28%5Cwidehat%7BAB%7D%29%2B160%2B60%3D360)
m(arc AB) = 360 - 220
= 140°
Therefore, this option is not correct.
Option (3),
![m(\widehat{ACB})=m(\widehat{AC})+m(\widehat{BC})](https://tex.z-dn.net/?f=m%28%5Cwidehat%7BACB%7D%29%3Dm%28%5Cwidehat%7BAC%7D%29%2Bm%28%5Cwidehat%7BBC%7D%29)
= 60° + 160°
= 220°
Option (3) is the correct option.
Option (4),
![m(\widehat{CBA})= 360-m(\widehat{AC})](https://tex.z-dn.net/?f=m%28%5Cwidehat%7BCBA%7D%29%3D%20360-m%28%5Cwidehat%7BAC%7D%29)
= 360° - 60°
= 300°
Therefore, this option is not correct.
Answer is: A. 0.50 [x + (x + 0.25x)], B. 0.50 (x + 1.25x), E.0.50 (2.25x)
30% decrease.
120-90 = 30