I have no idea how to do these?

Question

http://hometown.aol.com/amahol777/index.html

Answer 1

I am used to arcs being measured by the length of the arc s
s = r θ where θ is the measure of the central angle in radians.

However, the key thing to remember is that there are two ways to measure arcs. One is the mentioned above. The other way is as the measure of the central angle in degrees. Meaning
arc(AB) = θ where θ is the measure of the central angle in degrees.
Why is this? I do not know. It just is. With that in mind then if that is what is happening here, everything falls into place. I will start you off and you can continue.

Since we know that chord(AB) is a diameter then
arc(AB) = 180 = arc(AE) + arc(EB) = arc(AE) + 90
which implies arc(AE)=90
Also,
arc(AB) = 180 = arc(AC) + arc(CF) + arc(FB) = 45 + arc(CF) + 90 = 135 + arc(CF)
which implies arc(CF)=45

Angle1 = Angle2 = (1/2)(arc(AC) + arc(EB)) = (1/2)(45+90) = 135/2 = 67.5

Since lineBD is a tangent then Angle(ABD)=90
Angle3 = Angle(ABD) - Angle(ABF) = 90 - Angle(ABF)

But Angle(ABF) = (1/2)(central angle intercepting arc(AF))

Recall that your arcs are being measured by the measure of the central angle in degrees. So arc(AF) = 90 = central angle intercepting this arc.
Note it does not matter that the central angle is not drawn. You just need the value of the formula of Angle(ABF)
So Angle(ABF) = (1/2)90 = 45

So Angle3 = 90-45 = 45

...... and so on....
Hope that helps.

Answer 2

I do not see how to solve it without some assumptions.
Are the 90 degrees the arcs?
Is the 45 degree the arc?