For the all questions we use the theorem of chords and arcs and get that for the first question:
[tex]\measuredangle CEF=\text{ }\frac{1}{2}(30^{\circ}+58^{\circ})=44^{\circ}[/tex]
Now, to find angle D:
[tex]\measuredangle D=\frac{1}{2}(arcAB\text{ -arcGF)=}\frac{1}{2}(58^{\circ}-20^{\circ})=19^{\circ}[/tex]
Next for arcAC we use that WC and WA are tangent to the circle
O is the center of the circle ( O is not E). Now we recall that the inner angles of a quadrilateral is 360 so
[tex]\measuredangle\alpha=360-80-90-90=100[/tex]
By the definition of arcAC
[tex]arc\text{AC}=\measuredangle\alpha=100[/tex]
Finally we use the fact that the value of inscribed angles is half of the value of the central angle, using this we get :
[tex]\measuredangle EBD=\measuredangle CBG=\frac{1}{2}\measuredangle COG\text{ = }\frac{1}{2}(\text{arcFC}+\text{arcGF)}=\frac{1}{2}50^{\circ}=25^{\circ}[/tex]
