Question #5 in this PDF File

I know that AO, BO, CO, DO, are congruent to one another (radius) and that if I draw the lines AB, BC, and CD, that triangles AOB, BOC and COD are all isosceles.

It follows from the Isosceles Triangle Theorem that angle OAB = angle OBA = 60 degrees, so I know that triangle AOB is an equilateral triangle,

while angle OCD = angle ODC = 80 degrees.

However, I cannot see what I should do next. Can anyone help me? (a hint is fine. I think I have to show ABCO is a rhombus)

BONUS QUESTION: For question #3, is it as easy as I think it is? (2x + 2y = 180 => x + y = 90)