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:
[tex]\begin{gathered} EF=2\cdot\angle3 \\ EF=2\cdot49\degree \\ EF=98\degree \\ \\ \angle4=\frac{GH}{2} \\ \angle4=\frac{84}{2} \\ \angle4=42\degree \end{gathered}[/tex]b.
If ∠4 = 18°50' and EF = 105°, we have:
[tex]\begin{gathered} GH=2\cdot\angle4 \\ GH=2\cdot(18\degree50^{\prime}) \\ GH=36\degree100^{\prime}=37\degree40^{\prime} \\ \\ \angle3=\frac{EF}{2} \\ \angle3=\frac{105}{2} \\ \angle3=52.5\degree=52\degree30^{\prime} \end{gathered}[/tex]