1. **State the problem:** We have two identical, overlapping regular octagons (8-sided polygons) and need to find the size of the angle labeled $g$ formed at their intersection. 2. **Recall the formula for interior angles of a regular polygon:** The measure of each interior angle $I$ of a regular polygon with $n$ sides is given by $$I = \frac{(n-2) \times 180^\circ}{n}$$ 3. **Calculate the interior angle of one regular octagon:** For $n=8$, $$I = \frac{(8-2) \times 180^\circ}{8} = \frac{6 \times 180^\circ}{8} = \frac{1080^\circ}{8} = 135^\circ$$ 4. **Understand the angle $g$ formed by overlapping polygons:** The angle $g$ is formed between two edges of the overlapping octagons. Since the polygons are identical and regular, the angle between their edges at the intersection can be found by considering the exterior angle of the octagon. 5. **Calculate the exterior angle of the octagon:** The exterior angle $E$ is $$E = 180^\circ - I = 180^\circ - 135^\circ = 45^\circ$$ 6. **Determine angle $g$:** Because the polygons overlap and the angle $g$ is formed between two edges meeting at the intersection, $g$ equals the exterior angle of the octagon, $$g = 45^\circ$$ **Final answer:** $$\boxed{45^\circ}$$