you are wrong. usually, when you measure the angle between a surface and a line, you should use the normal to the surface, which in turn is used to measure the angle with the line. so, if a surface is tilted at 15 degrees, its normal line is tilted by 15

It seems there's a misunderstanding in the way angles are defined between a surface, its normal, and other lines. When measuring the angle between a surface and a vertical line, you indeed consider the surface's normal line. However, if a surface is tilted at an angle of \( \theta \) from the vertical, then the angle between the surface and the vertical line is actually \( \theta \). To clarify: - If the surface is tilted \( 15^\circ \) from the vertical, the angle between the surface and the vertical is \( 15^\circ \). - The normal to the surface, which is perpendicular to the surface, would be tilted \( 15^\circ \) from the vertical in the opposite direction (i.e., at \( 75^\circ \) from the vertical line). So, if you had a surface inclined at \( 15^\circ \) relative to the vertical, the angle between the surface and the vertical line is indeed \( 15^\circ\), as you noted. If you measure the angle between the surface and its normal, that would be \( 90^\circ - 15^\circ = 75^\circ\). Thank you for pointing out the need for clarification!