1. The problem is to find the measure of each interior angle of a regular octagon (8-sided polygon). 2. We know the number of sides $n=8$ and the sum of exterior angles of any polygon is always 360 degrees. 3. The sum of interior angles formula is $$180(n-2)$$. 4. Substituting $n=8$, we get $$180(8-2) = 180 \times 6 = 1080$$ degrees for the sum of all interior angles. 5. Since it's a regular octagon, all interior angles are equal, so each interior angle is $$\frac{1080}{8} = 135$$ degrees. 6. The exterior angle at each vertex, which is adjacent to the interior angle, is $$\frac{360}{8} = 45$$ degrees. 7. The question mark in the green box represents the interior angle, which we found to be 135 degrees. Final answer: Each interior angle of the regular octagon is $135$ degrees.