1. **State the problem:** We need to find the measure of one interior angle of a regular octagon. 2. **Formula used:** The sum of interior angles of a polygon with $n$ sides is given by $$180(n-2)$$ degrees. 3. **Important rule:** In a regular polygon, all interior angles are equal, so one interior angle is the total sum divided by the number of sides. 4. **Calculate the sum of interior angles for an octagon:** $$180(8-2) = 180 \times 6 = 1080$$ degrees. 5. **Find one interior angle:** $$\frac{1080}{8} = 135$$ degrees. 6. **Conclusion:** Each interior angle of a regular octagon measures $135$ degrees.