1. **State the problem:** We have a quadrilateral with angles at vertices F, M, S, and G. The angles at M, S, and G are given as 85°, 127°, and 62° respectively. We need to find the unknown angle $y$ at vertex F. 2. **Formula used:** The sum of interior angles in any quadrilateral is always 360°. This is a key rule for polygons. 3. **Set up the equation:** Let the angles be $y$ (at F), 85° (at M), 127° (at S), and 62° (at G). Then, $$y + 85 + 127 + 62 = 360$$ 4. **Calculate the sum of known angles:** $$85 + 127 + 62 = 274$$ 5. **Solve for $y$:** $$y + 274 = 360$$ $$y = 360 - 274$$ $$y = 86$$ 6. **Answer:** The unknown angle $y$ at vertex F is 86°. This means the quadrilateral's angles add up correctly to 360°, confirming our solution.