1. **State the problem:** We are given three intersecting lines forming angles around a point. Two angles are given: 77° and 70°, and we need to find the value of angle $w$. 2. **Recall the rule:** The sum of all angles around a point is always 360°. 3. **Identify the angles:** The three given angles around the point are 77°, 70°, and $w$. The remaining angle adjacent to $w$ is vertically opposite to 77° and thus also 77°. 4. **Set up the equation:** The sum of the four angles around the point is $$77 + 70 + w + 77 = 360$$ 5. **Simplify the equation:** $$77 + 70 + 77 + w = 360$$ $$224 + w = 360$$ 6. **Solve for $w$:** $$w = 360 - 224$$ $$w = 136$$ 7. **Final answer:** The value of $w$ is **136°**.