Geometry Inscribed Angles and Central Angles Help

[Guest]

Hi! I would appreciate it if you could help me out with this problem having to do with determining the values of angles (1-35) in the circle. The diagram/given is this:
Thank you in advance; it's due tonight and I have no idea where to start!

[Guest]

There are three ways lines and circles can meet to form angles and arcs.
1. Two lines can cross inside the circle, forming a total of four angles and cutting the circle into four arcs.
Two opposite angles are the same measure of course and that measure is the average of the measures of the two arcs. In this case, for example, the measure of angle #31 is (m(BC)+ m(RS))/2.

2. Two lines cross on the circle, forming one angle and crossing the circle in one arc. The measure of the angle is half the angle of the arc. In this case, for example, the measure of angle 29 is m(RS)/2.

3. Two lines cross outside the circle,crossing the circle in four points, making one angle and two arcs. The measure of the angle is half the difference of the two arcs. In this case, the measure of angle BQC is half the measure of arc BC minus the measure of arc RS. We are told that angle BQC has measure 18 degrees. It cuts the circle in arc BC that has measure 76 degrees and in arc RS. Calling the measure of arc RS "[tex]\theta[/tex]" we have [tex]\frac{76- \theta}{2}= 18[/tex]. So [tex]76- \theta= 36[/tex]. [tex]\theta= 76- 36= 40[/tex] degrees. Angle #29, angle RCS, is half of that, 20 degrees. Continue like that.