If a piece of flat stock is to be bent to form a closed angle of 15°, through what angle must it be bent?

When bending a piece of flat stock to create a closed angle, the relationship between the angle being formed and the angle through which the material is bent is critical. The angle through which the material must be bent is actually based on the need to account for the resulting shape of the bent material.

To achieve a closed angle of 15°, you need to consider that each side of the bend contributes to the total angle. The total angle around the bend must sum to 360°, but since you're specifically forming a 15° angle, you need the material to travel across both legs of the angle that it creates.

Each side of the bend will 'consume' an angle—meaning that if you want a 15° angle in the final shape, you effectively need to bend the stock through more than just 15 degrees. This is because you're laying out the flat material in addition to the angle you're closing off. Therefore, when bending to form an angle, you would typically bend it greater than the angle you wish to create, leading to the conclusion that you must bend it through 165°.

Thus, the correct answer is 165°, which accounts for the necessary additional degrees to create the closed angle of 15°. Understanding this relationship is key