m < AOB = 90 degrees. Reason:- Triangle ABC is isosceles and AO = AC.
m < BOC = 90 degrres Reason:- Its adjacent to < AOB
m < BOK = 1/2 * m < BOC = 45 degrees Reason: OK bisects <BOC
Therefore m < AOK = m AOB + m < BOK = 90 + 45
= 135 degrees (answer)