Question

Given: BD is a diameter m 1 = 100° m BC = 30° m AC = 60 110 200

Answer 1

Answer:

110°

Step-by-step 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)

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

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