Question 1956
     You are right arc ACD having the 1 dim length not an angle,but the  
  permeter of the whole circle is 360 deg, so an arc of 200 deg means an arc 
  of length 2 pi r * 200/360. Let O be the center of the circle. 
  Degree of Arc ACD = degree of the angle AOD(facing the arc ACD). 

      P
  
     B  D
    A    C

  Now, arc ACD = 200 deg =arc BAC 
  arc ABD = 160 deg ((= 360 -200) = arc BDC
  angle ACD = half of arc ABD = 160 * 1/2 = 80 deg
  Similarly, angle BAC = 80 deg
  Hence, in the triangle APC,  we see that 
  angle APC = 180 - 80*2 = 20 deg 

  Kenny