Use algebra for such problems let, Angle COD = x Angle KOD = y Angle KPC = z Given ,. x - y = 61° ( Equation 1 ) x - z = 53° ( Equation 2 ) Subtract 1st equation from 2nd and you'll get :
z - y = 8° ( Equation 3 ) Now since , x + y + z = 180° ( Equation 4 ) Add Equation 3 to Equation 4 and you'll get x + 2z = 188° ( Equation 5) From Equation 2 we know that , x -z = 53° or, x = 53° + z ( Equation 6 ) Put this value of 'x' in Equation 5 and solve for z. you'll get : (53° + z) + 2z = 188° or 3z = 188 - 53 = 135° solving for z we get z = 45° put this value of z in Equation 5 x + ( 2 x 45° ) = 188° or x = 188° - 90° = 98° hence , Angle COD = 98°
