Anyone really good with Geometry and Circles? Dealing with arcs and angles?

Question

Look at the following picture:

http://s37.photobucket.com/albums/e82/cmartinfs/?action=view¤t=mathcirlcle.jpg

and help me find the measure of each angle. the angles are labeled with numbers 1-10. Help Please! and if you could possibly tell me how you got your answer that would be most helpful. Just Remember that I need to know all the angles 1-10. Thanks

Answer 1

angle 5 = 1/2(arc AC-arc EG) = 1/2(120-58)= 31 degrees
angle 3 = 1/2 arcAE = 1/2(84) = 42 degrees
angle 8 = arc AC = 120 degrees
angle 9 = 1/2(arcAEC-arcAC) = 1/2(240-120) = 60 degrees
angle 1 = 180-angle 8 = 180-120 = 60 degrees
Since angle 1 = 60 degrees, arc BC = 60 degrees and it follows
that arc BG = 48 degrees.
angle 2 = 90 degrees since it intercepts a diameter
angle FEB = 180 - angle 2=180- 90 = 90 degrees
angle 6 = angle 5 + angle FEB = 31+ 90 = 121 degrees
angle 4= 360-121-85-53 = 101 degrees
angle 7 = angle 4 -angle 1 = 101 - 60 = 41 degrees
angle 10 = 1/2 arcGC = 1/2 (108) = 54 degrees

Answer 2

angle 2 is 90 degrees, because AB is the diameter of the circle and E is on the circle., as point E moves over the circle, the angles stays 90 degrees.

angle 8 is 120 dgress, this is just given ? since arc AC is 120 degrees.
thus angel 1 is 60 degrees (adds up to 180 degrees)

angle 5 is 58 degrees is just given : arc EG is 58

AOE = 84 thus OAE = (180-84) / 2 = 48 degrees so angle3 is 180 - 48 - 90 = 42

180 - 58 - 90 = 22 => angle6=180-22=158
180 - 22 - 42 = 126 = angle4
60+angle7=180-angle4=126 => angle7=66
angle10+angle7=90=>angle10=90-66=24
resume
angle1 = 60
angle2 = 90
angle3 = 42
angle4=126
angle5=58
angle6=158
angle7=66
angle8 = 120
angle9=you can do that yourself
angle10=24