Answer:
110°
Step-by-step explanation:
[tex] m\angle 1 + m\angle 2 = 180\degree [/tex]
(linear pair angles)
[tex] 100\degree + m\angle 2 = 180\degree [/tex]
[tex] m\angle 2 = 180\degree- 100\degree [/tex]
[tex] m\angle 2 = 80\degree [/tex]
[tex] \because m\widehat {AB} =m\angle 2 [/tex]
(Measure of the minor arc is equal to the corresponding central angle)
[tex] \therefore m\widehat {AB} = 80\degree [/tex]
[tex] \because m\widehat {AC} =m\widehat {AB} +m\widehat {BC}[/tex]
(By arc sum property)
[tex] \therefore m\widehat {AC} = 80\degree+30\degree [/tex]
[tex] \huge \red {\boxed {\therefore m\widehat {AC} = 110\degree}} [/tex]
