1. **State the problem:** We have a triangle with angles labeled as $45^\circ$, $11w$, and $16w$. We need to find the value of $w$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles of any triangle is always $180^\circ$. So, $$45 + 11w + 16w = 180$$ 3. **Combine like terms:** $$45 + 27w = 180$$ 4. **Isolate $w$:** Subtract 45 from both sides: $$27w = 180 - 45$$ $$27w = 135$$ 5. **Solve for $w$:** Divide both sides by 27: $$w = \frac{135}{27} = 5$$ **Final answer:** $$w = 5^\circ$$