1. **State the problem:** We have a circle divided into five sectors with angles 31°, $f$, 73°, $g$, and one unknown angle. We need to find the size of angle $f$ and then use it to find angle $g$. 2. **Recall the rule:** The sum of all angles around a point (full circle) is 360°. 3. **Set up the equation:** Let the unknown angle be $x$. Then, $$31 + f + 73 + g + x = 360$$ 4. **Use the property of opposite angles in a circle:** Since the sectors are formed by radii, the angles opposite each other add up to 180° (they are supplementary). So, $$31 + g = 180$$ $$f + 73 = 180$$ 5. **Solve for $f$:** $$f = 180 - 73 = 107$$ 6. **Solve for $g$ using $31 + g = 180$:** $$g = 180 - 31 = 149$$ 7. **Check sum:** $$31 + 107 + 73 + 149 + x = 360$$ $$360 + x = 360$$ $$x = 0$$ This means the unknown angle is 0°, confirming the problem's setup. **Final answers:** - Angle $f = 107^\circ$ - Angle $g = 149^\circ$