What is the measure of the missing angle?

137 degrees

Step-by-step explanation:

By using the fact that a triangle contains 180 degrees and angles made by the same lines are congruent we can find out that the top angle in the first triangle is 45 degrees. We can then figure out that the missing angle in that same triangle is 75 degrees by adding 45 and 60 and subtracting that from 180. Then we add that 75 degrees to 68 degrees to get 143 degrees which we can use to discover that the corner of the triangle that connects to the other triangle is 37 degrees. From there we know that triangles contain 180 degrees, so the remaining value is 43 and with this we can discover that the value of the asked for angle is 137 degrees.