1. **State the problem:** We are given a triangle with angles labeled as $3x$, $2x$, and $x + 30$. We need to find the size of the largest angle. 2. **Recall the rule:** The sum of the interior angles of a triangle is always $180^\circ$. So, $$3x + 2x + (x + 30) = 180$$ 3. **Simplify the equation:** $$3x + 2x + x + 30 = 180$$ $$6x + 30 = 180$$ 4. **Isolate $x$:** $$6x = 180 - 30$$ $$6x = 150$$ 5. **Solve for $x$:** $$x = \frac{150}{6}$$ $$x = 25$$ 6. **Find each angle:** - $3x = 3 \times 25 = 75^\circ$ - $2x = 2 \times 25 = 50^\circ$ - $x + 30 = 25 + 30 = 55^\circ$ 7. **Identify the largest angle:** The largest angle is $75^\circ$. **Final answer:** The largest angle measures $75^\circ$.