Question

Determine the number of degrees for each arc or angle?

Answer 1

The angles ∠3 and ∠4 are inscribed angles.

The angle ∠3 inscribes the arc EF, and the angle ∠4 inscribed the arc GH.

An inscribed angle has half the measure of the inscribed arc.

a.

So, if ∠3 = 49° and GH = 84°, we have:

`\begin{gathered} EF=2\cdot\angle3 \\ EF=2\cdot49\degree \\ EF=98\degree \\ \\ \angle4=(GH)/(2) \\ \angle4=(84)/(2) \\ \angle4=42\degree \end{gathered}`

b.

If ∠4 = 18°50' and EF = 105°, we have:

`\begin{gathered} GH=2\cdot\angle4 \\ GH=2\cdot(18\degree50^(\prime)) \\ GH=36\degree100^(\prime)=37\degree40^(\prime) \\ \\ \angle3=(EF)/(2) \\ \angle3=(105)/(2) \\ \angle3=52.5\degree=52\degree30^(\prime) \end{gathered}`