Geometry... again!! I think I got number 8, but 9 is confusing me
For 9b: Since you already know that DC is 145 and BC is 110, subtract to get DB
For 9e: I'm not sure if you've already learned this, but there is a formula that every angle formed from a point on a circle and two points on opposite ends of a diameter is a 90 degree angle. You can probably look it up to get a proof if you need one. So, that makes angle ABC 90 degrees. Therefore, BAC and ACB add up to 90 degrees, and since BAC is 55 you know that angle C is 35.
For 9f: As aforestated in 9e, 90 degrees. I don't have the proof memorized, but you can look it up.
For 9g: You know what AD is, and because of the Vertical Angles Theorem both angles DOA and COE are the same size, meaning that arc CE is the same length as AD.
For 9h: This is 180 degrees minue CE.
Hope this was helpful! :)
a. m∠AOD = m arc AD = 35
b. DO bisects ∠AOB, so m∠DOB = m∠AOD = 35 = m arc DB
c. m∠AOD + m∠DOB + m∠BOC = 180
35 + 35 + m∠BOC = 180 → m∠BOC = 180 - 35 - 35 = 110 = m arc BC
d. m∠A + 90 + m∠AOD = 180
m∠A + 90 + 35 = 180 → m∠A = 180 - 90 - 35 = 55
e. m∠C = (1/2) * m arc BA
m∠C = (1/2) * (35 + 35) = 35
f. Since m∠AOD = m∠C , DE is || to BC... and so m∠AFO = m∠B = 90
g. m∠COE = m∠AOD = 35 = m arc CE
h. m arc AE = 180 - m arc CE = 180 - 35 = 145
Looks like my answers agree with yours!
Also I checked your number 8 and I agree with all your answers for it!