1. **State the problem:** Given a triangle with angles 3 and 4 measuring 125° and 23° respectively, find the measure of angle 2. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of a triangle is always 180°. 3. **Write the equation:** $$\text{angle 2} + \text{angle 3} + \text{angle 4} = 180$$ 4. **Substitute known values:** $$\text{angle 2} + 125 + 23 = 180$$ 5. **Simplify the sum of known angles:** $$125 + 23 = 148$$ 6. **Rewrite the equation:** $$\text{angle 2} + 148 = 180$$ 7. **Isolate angle 2:** $$\text{angle 2} = 180 - 148$$ 8. **Calculate the value:** $$\text{angle 2} = 32$$ **Final answer:** The measure of angle 2 is $32^\circ$.