Answer:
80°
Step-by-step explanation:
AB and AC are chords.
Chords AB and AC are at a distance of 2 units from the center of the circle.
-> Chord AB = Chord AC
[tex]\implies m(\widehat {AB})=m(\widehat {AC})[/tex]...(1)
(Equal chords intercept equal arcs)
[tex]m(\widehat {AB})+m(\widehat {AC})+m(\widehat {BC})=360\degree[/tex]
(By arc sum property of a circle)
[tex]\implies m(\widehat {AB})+m(\widehat {AB})+200\degree=360\degree[/tex]
(From equation 1)
[tex]\implies 2m(\widehat {AB})=360\degree-200\degree[/tex]
[tex]\implies 2m(\widehat {AB})=160\degree[/tex]
[tex]\implies m(\widehat {AB})=\frac{160\degree}{2}[/tex]
[tex]\implies \huge{\orange{m(\widehat {AB})={80\degree}}}[/tex]
