1. The problem asks for the size of the reflex angle given a smaller angle of approximately 45 degrees. 2. Recall that a reflex angle is the larger angle formed by two rays, greater than 180 degrees but less than 360 degrees. 3. The total degrees around a point is 360 degrees. 4. The smaller angle is given as $45^\circ$. 5. To find the reflex angle, subtract the smaller angle from 360 degrees: $$\text{Reflex angle} = 360^\circ - 45^\circ$$ 6. Calculate the subtraction: $$360^\circ - 45^\circ = 315^\circ$$ 7. Therefore, the size of the reflex angle to the nearest degree is $315^\circ$.