Question

Given: BD is a diameter

m 1 = 100°
m BC = 30°
m AC =

60
110
200

Answer 1

110°

Explanation:

`m\angle 1 + m\angle 2 = 180\degree`

(linear pair angles)

`100\degree + m\angle 2 = 180\degree`

`m\angle 2 = 180\degree- 100\degree`

`m\angle 2 = 80\degree`

`\because m\widehat {AB} =m\angle 2`

(Measure of the minor arc is equal to the corresponding central angle)

`\therefore m\widehat {AB} = 80\degree`

`\because m\widehat {AC} =m\widehat {AB} +m\widehat {BC}`

(By arc sum property)

`\therefore m\widehat {AC} = 80\degree+30\degree`

`\huge \red {\boxed {\therefore m\widehat {AC} = 110\degree}}`