To solve this question, we need to find the angle that the line with equation $y = -x + 4$ makes with the positive direction of the x-axis.

Step-by-Step Explanation:

1. Line Equation Form: The equation of the line is $y = -x + 4$, which can be written in the slope-intercept form: $y = mx + b$ where $m$ is the slope of the line, and $b$ is the y-intercept.

   In this case, $m = -1$ and $b = 4$.

2. Relationship Between Slope and Angle: The slope $m$ of the line is related to the angle $\theta$ it makes with the positive x-axis by the formula: $m = \tan(\theta)$ So, we have: $\tan(\theta) = -1$

3. Find the Angle: To find $\theta$, we use the inverse tangent (arctan) function: $\theta = \tan^{-1}(-1)$ This gives us an angle of $\theta = -45^\circ$. However, this is a negative angle, measured clockwise from the positive x-axis. To find the corresponding positive angle (measured counterclockwise), we add $180^\circ$: $\theta = 180^\circ - 45^\circ = 135^\circ$

Therefore, the angle that the line makes with the positive x-axis is 135°.

Correct Answer: C (135°)

Would you like further details or explanations on any step? Here are some related questions to deepen your understanding:

1. How does the slope of a line affect the angle it makes with the x-axis?
2. What is the significance of the negative sign in the slope of a line?
3. How can you find the angle for a line with a positive slope?
4. What is the general procedure to convert a negative angle to a positive angle?
5. How would the answer change if the slope was different, say $m = -2$?

Tip: Remember, if a line's slope is negative, the angle it makes with the x-axis will always be greater than $90^\circ$ but less than $180^\circ$.