The measure of angle KLB is 30 degrees.

To find the measure of angle, I used the theorem which states that the sum of the remote interior angles is equal to the exterior angle.

The exterior angle for triangle ALB is 40 degrees, so angle ALB is 140 degrees. Similarly, the exterior angle for triangle AKC, so angle AKC is 130.

Finding all of the missing angles is fun! But on to the question...

More deductions give KLB = AKL - 20. So, if AKL is 20, then KLB would be no degree measure. If AKL is 30 degrees then KLB would be 10 degrees.If AKL is 40, then KLB would be 20. If AKL is 50, then KLB would be 30.

Part II:

The measure of angle ACM is 10 degrees.