1. **State the problem:** We have a triangle with angles labeled as $3w$, $2w$, and $35^\circ$. 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, $$3w + 2w + 35 = 180$$ 3. **Combine like terms:** $$5w + 35 = 180$$ 4. **Isolate $w$:** $$5w = 180 - 35$$ $$5w = 145$$ 5. **Solve for $w$:** $$w = \frac{145}{5} = 29$$ 6. **Final answer:** $$w = 29^\circ$$ This means the value of $w$ is 29 degrees.