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Sagot :
a.
The angle ∠1 inscribes the arc AB, so its measure is half the measure of the arc, so we have:
[tex]\begin{gathered} \angle1=\frac{AB}{2} \\ \angle1=\frac{122\degree24^{\prime}}{2} \\ \angle1=61\degree12^{\prime} \end{gathered}[/tex]b.
Since AC is the diagonal of the circle, the arc AC has 180°.
Angle ∠2 inscribes this arc, so we have:
[tex]\begin{gathered} \angle2=\frac{AC}{2} \\ \angle2=\frac{180}{2} \\ \angle2=90\degree \end{gathered}[/tex]c.
In order to find arc BC, we can sum all three arcs and make it equal 360°:
[tex]\begin{gathered} AB+BC+AC=360\degree \\ 122\degree24^{\prime}+BC+180\degree=360\degree \\ BC=360\degree-180\degree-122\degree24^{\prime} \\ BC=57\degree36^{\prime} \end{gathered}[/tex]
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