how to find an angle?

[marinaa11]

Hello, I am in trouble with this task:
I have to find an angle D and angle COA (O).
My ideas: I know, that the measure of an inscribed angle is half the measure of the intercepted arc, but I need to find angle COA and only then I will be able to find an angle D. As angles C and A are inscribed in the same arc, they are the same measure?
Could you give me some hints about this task?
Thank you.

 

[Harry_the_cat]

Using the circle theorem that you mentioned, what is the measure of angle COA (on the left hand side where the O is)?

 

[HallsofIvy]

Yes, arc CDA is 2(58)= 116 degrees so angle COA is 116 degrees. Now, what is the measure of arc ABC and, from that, what is the measure of angle D?

 

[marinaa11]

D is 122 degrees, thank you!