Given that angle $EFD$ is in standard position and its terminal side passes through the point $\left(8,8\right)$, what is the measure of angle $EFD$ to the nearest half degree?

• A. $37.5°$
• B. $45°$
• C. $47.5°$
• D. $55°$

Answer: (B)

Verified step by step guidance

1. Identify that the angle \( \angle EFD \) is in standard position, meaning its vertex is at the origin and its initial side lies along the positive x-axis.
2. Recognize that the terminal side of the angle passes through the point \( (8, 8) \), which lies in the first quadrant.
3. Use the coordinates of the point to find the slope of the terminal side, which is \( \frac{y}{x} = \frac{8}{8} = 1 \).
4. Recall that the tangent of the angle \( \theta \) formed by the terminal side with the positive x-axis is equal to the slope, so \( \tan(\theta) = 1 \).
5. Find the angle \( \theta \) by taking the inverse tangent (arctangent) of 1, i.e., \( \theta = \tan^{-1}(1) \), and then round the result to the nearest half degree.