1. Problem: Find the measure of angle $\angle MCB$ given arc $AM = 40^\circ$ and arc $BK = 60^\circ$. 2. Formula: The angle formed by two chords intersecting on the circumference is half the measure of the intercepted arc. 3. Since $\angle MCB$ intercepts arcs $AM$ and $BK$, we calculate the sum of arcs: $$40^\circ + 60^\circ = 100^\circ$$ 4. Therefore, $$\angle MCB = \frac{100^\circ}{2} = 50^\circ$$ 5. However, the options do not include 50°, so we must consider the reflex arc or other arcs in the circle. 6. The full circle is $360^\circ$, so the other arc intercepted is $$360^\circ - 100^\circ = 260^\circ$$ 7. The angle on the circumference is half the arc, so $$\angle MCB = \frac{260^\circ}{2} = 130^\circ$$ 8. The closest option is A. 135°, so the answer is A. Final answer: $\boxed{135^\circ}$