1. **State the problem:** We have a kite-shaped quadrilateral FGHI with angles at G and I given as 88° and 106° respectively. We need to find the measure of angle F, denoted as $m\angle F$. 2. **Recall the property of quadrilaterals:** The sum of interior angles in any quadrilateral is always 360°. 3. **Write the equation for the sum of angles:** $$m\angle F + m\angle G + m\angle H + m\angle I = 360^\circ$$ 4. **Use kite properties:** In a kite, two pairs of adjacent sides are equal, and the angles between unequal sides are equal. Here, sides FI and IH are equal, and sides FG and GH are equal, so angles at F and H are equal. 5. **Set $m\angle F = m\angle H = x$:** 6. **Substitute known values and variables:** $$x + 88^\circ + x + 106^\circ = 360^\circ$$ 7. **Simplify the equation:** $$2x + 194^\circ = 360^\circ$$ 8. **Isolate $x$:** $$2x = 360^\circ - 194^\circ$$ $$2x = 166^\circ$$ 9. **Divide both sides by 2:** $$x = \frac{166^\circ}{2}$$ $$x = 83^\circ$$ 10. **Conclusion:** $$m\angle F = 83^\circ$$