1. The problem asks to find the measure of each interior angle of the shelf and the sum of the interior angles. 2. The formula for the sum of interior angles of a polygon with $n$ sides is: $$\text{Sum of interior angles} = (n - 2) \times 180^\circ$$ 3. Since the shelf is represented as a rectangle, it has $n = 4$ sides. 4. Substitute $n = 4$ into the formula: $$\text{Sum of interior angles} = (4 - 2) \times 180^\circ = 2 \times 180^\circ = 360^\circ$$ 5. Each interior angle of a rectangle is equal, so divide the sum by 4: $$\text{Each interior angle} = \frac{360^\circ}{4}$$ 6. Simplify the fraction: $$\text{Each interior angle} = \cancel{\frac{360^\circ}{4}} = 90^\circ$$ 7. Therefore, the sum of the interior angles is $360^\circ$ and each interior angle measures $90^\circ$.