If an angle in standard position has its terminal side passing through the point $(1,2)$, which of the following is closest to the measure of the angle in degrees?

• A. $63°$
• B. $95°$
• C. $25°$
• D. $45°$

Answer: (A)

Verified step by step guidance

1. Identify the coordinates of the point through which the terminal side of the angle passes. Here, the point is (1, 2).
2. Recall that the angle \( \theta \) in standard position can be found using the tangent function, where \( \tan(\theta) = \frac{y}{x} \). Substitute the coordinates: \( \tan(\theta) = \frac{2}{1} = 2 \).
3. Use the inverse tangent function to find the angle: \( \theta = \tan^{-1}(2) \). This will give the angle in radians or degrees depending on your calculator settings.
4. Make sure your calculator is set to degrees mode to find the angle in degrees.
5. Compare the calculated angle to the given options and select the one closest to your result.