Here is my way of solving problem 1. Instead of trying to solve it, I try to move points around in my imagination. I make sure what I know is static, and check if I can move around stuff I dont know. Here is problem 1:

(1) alone: COD is 60 degrees, but we can move point B around. Hence chance angle BAP.
(2) alone: BCO is 40 degrees. Only point O is fixed, we can move B and C around as long as BCO is 40 degrees, hence we change angle BAO.

Soln for problem 2

We have 2 right angled triangles. Let us find the third side for both these triangles.

For triangle with sides 3 and 4 , the third side has length 5
For triangle with sides 13 and 12 , the third side has length 5

Hence our triangle with angle x is actually an isosceles triangle with 2 sides equal to 5.

Hence the other base angle = 55

Hence x= 180 - (55 + 55) = 70


I could not solve problem 1. . Need help..