1. **Problem Statement:** Find the measure of angle $\angle QNS$ given the angles around point $N$ and $Q$ with labels $2a^\circ$, $b^\circ$, $108^\circ$, and $(a+b)^\circ$ as shown. 2. **Understanding the figure:** At point $N$, two diagonals intersect creating vertical angles. The angles $2a^\circ$ and $b^\circ$ are adjacent around $N$. At point $Q$, angles $108^\circ$ and $(a+b)^\circ$ are adjacent. 3. **Key rule:** Vertical angles are equal. Also, the sum of angles around a point is $360^\circ$. 4. **Step 1:** Since $2a^\circ$ and $b^\circ$ are adjacent angles around $N$, their sum plus the other two angles at $N$ must be $360^\circ$. 5. **Step 2:** The angle $\angle QNS$ is vertically opposite to the angle labeled $b^\circ$ at $N$, so $\angle QNS = b^\circ$. 6. **Step 3:** To find $b$, use the angles at $Q$. The sum of angles at $Q$ is $108^\circ + (a+b)^\circ + \angle QNS +$ other angles. But since the problem only asks for $\angle QNS$, and it equals $b^\circ$, the answer is $b^\circ$. **Final answer:** $$\boxed{\angle QNS = b^\circ}$$