1. **State the problem:** We are given that the sum of the interior angles of a regular polygon is 1440 degrees. We need to find the size of each exterior angle of this polygon. 2. **Formula for sum of interior angles:** The sum of the interior angles $S$ of a polygon with $n$ sides is given by: $$S = 180(n - 2)$$ 3. **Find the number of sides $n$:** Given $S = 1440$, substitute and solve for $n$: $$1440 = 180(n - 2)$$ Divide both sides by 180: $$\frac{1440}{180} = n - 2$$ $$8 = n - 2$$ Add 2 to both sides: $$n = 10$$ 4. **Find the size of each exterior angle:** The exterior angle of a regular polygon is given by: $$\text{exterior angle} = \frac{360}{n}$$ Substitute $n=10$: $$\text{exterior angle} = \frac{360}{10} = 36$$ **Final answer:** Each exterior angle of the polygon is $36$ degrees.