Question

When arc AB= 122°24', determine the number of degrees for each arc or angle?

Answer 1

a.

The angle ∠1 inscribes the arc AB, so its measure is half the measure of the arc, so we have:

`\begin{gathered} \angle1=(AB)/(2) \\ \angle1=(122\degree24^(\prime))/(2) \\ \angle1=61\degree12^(\prime) \end{gathered}`

b.

Since AC is the diagonal of the circle, the arc AC has 180°.

Angle ∠2 inscribes this arc, so we have:

`\begin{gathered} \angle2=(AC)/(2) \\ \angle2=(180)/(2) \\ \angle2=90\degree \end{gathered}`

c.

In order to find arc BC, we can sum all three arcs and make it equal 360°:

`\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}`