In the given figure BC id diameter O is center <BAO is 65^o find <AOC and <ADC

triangle AOB is an isoceles triangle (AO=BO) 
therefore angle ABO=65⁰
by angle sum property we can find angle AOB which is 50⁰ 
diameter is always a straight line
therefore angle AOB+angle AOC=180⁰
                       50⁰+angle AOC=180⁰
                               angle AOC=130⁰
 Now angle ADC is half of angle AOC
​therefore angle ADC =65⁰