Given that
[tex]m\angle ABC[/tex]
is equal to one half of
[tex]\text{m}\hat{\text{AC}}[/tex]
we can set the following equation:
[tex]\text{m}\hat{\text{AC}}=2m\angle ABC.[/tex]
Now, substituting the given value for m∠ABC, we get:
[tex]\text{m}\hat{\text{AC}}=2\times40^{\circ}=80^{\circ}.[/tex]
Finally, notice that:
[tex]m\hat{\text{ABC}}=360^{\circ}-m\hat{AC}.^{}[/tex]
Therefore:
[tex]\text{m}\hat{\text{ABC}}=280^{\circ}.[/tex]
Answer:
Part I:
[tex]\text{arcAC}=2\times\angle B.[/tex]
Part II:
[tex]\text{m}\hat{\text{AC}}=80^{\circ}.[/tex]
Part III:
[tex]\text{m}\hat{\text{ABC}}=280^{\circ}.[/tex]
