See the attached image. What you have so far is correct. You'll use the two parallel lines to use the alternate interior angle theorem. This is shown by the two red angles in the diagram. Based on that we know...
angle CRK = angle RCI = 44 degrees
Then you'll use the fact that triangle RCK is isosceles, so angle K is also 44 degrees
Afterward, use a bit of algebra to find angle RCK = 92 degrees. More specifically, you'll solve x+44+44 = 180 to get x = 92
Finally add up 44 and 92 to get 136 as the answer