1. The problem asks to find the size of angle $ABC$ in a triangle where angle $A$ is $72^\circ$ and angle $C$ is $37^\circ$. 2. Recall that the sum of the interior angles in any triangle is always $180^\circ$. 3. Use the formula for the sum of angles in a triangle: $$\text{angle } A + \text{angle } B + \text{angle } C = 180^\circ$$ 4. Substitute the known values: $$72^\circ + \text{angle } B + 37^\circ = 180^\circ$$ 5. Combine the known angles: $$109^\circ + \text{angle } B = 180^\circ$$ 6. Solve for angle $B$: $$\text{angle } B = 180^\circ - 109^\circ = 71^\circ$$ 7. Therefore, the size of angle $ABC$ is $71^\circ$.