1. The problem asks to find the size of angle $d$ in a regular octagon and to explain Sonia's mistake. 2. Sonia calculated $d$ as $\frac{360}{8} = 45^\circ$. This is correct for the exterior angle of a regular octagon because the sum of exterior angles of any polygon is $360^\circ$, and dividing by the number of sides (8) gives each exterior angle. 3. However, the question asks for the size of angle $d$, which is marked as an interior angle, not an exterior angle. 4. The interior angle $d$ of a regular polygon is related to the exterior angle by: $$d = 180^\circ - \text{exterior angle}$$ 5. Since the exterior angle is $45^\circ$, the interior angle $d$ is: $$d = 180^\circ - 45^\circ = 135^\circ$$ 6. Therefore, Sonia's mistake was assuming $d$ was the exterior angle when it is actually the interior angle. 7. Final answer: $$d = 135^\circ$$