1. ## Find Alpha

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)

2. It is a little long to write so I give you a hint and when you're stuck ask again.
The hint is :
Consider the isosceles triangle ACO. Say its identic angles are ... x (or any variable you want). Then start expressing all the angles with respect to x. You can start by the one between the 60 degree angle and the 20 degree angle. It will give you 120 - 2x. Keep doing that and you will find that supplementary angle of alpha is 40. It follows that alpha is 140 degree (if I made no mistakes )

3. That was an evil question lol! The rest of what I got didn't even matter... I thought I was going around in circles! That is, until I got a number valued angle when the variable canceled out in a smaller triangle... dude. DUDE!