let's suppose a surface is tilted at 15 degress. what is the angle that the surface makes with a vertical line?

If a surface is tilted at an angle of 15 degrees from the horizontal, the angle that the surface makes with a vertical line can be calculated as follows: Since the total angle around a point is 90 degrees (the angle between the horizontal and vertical lines), you can find the angle the surface makes with the vertical by subtracting the tilt angle from 90 degrees: \[ \text{Angle with vertical} = 90^\circ - \text{Tilt angle} \] Substituting the tilt angle: \[ \text{Angle with vertical} = 90^\circ - 15^\circ = 75^\circ \] So, the angle that the surface makes with a vertical line is 75 degrees.