If an angle $\mathrm{lkj}$ in standard position has a terminal side that passes through the point $(7,6)$ on the coordinate plane, what is the measure of angle $\mathrm{lkj}$ in degrees, rounded to the nearest whole degree?

• A. $49°$
• B. $55°$
• C. $45°$
• D. $41°$

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 (7, 6).
2. Recall that the angle \( \theta \) in standard position can be found using the tangent function, since \( \tan(\theta) = \frac{y}{x} \) where \( (x, y) \) are the coordinates of the point.
3. Calculate the ratio \( \frac{y}{x} = \frac{6}{7} \). This ratio represents \( \tan(\theta) \).
4. Use the inverse tangent function (arctangent) to find the angle \( \theta = \tan^{-1}\left(\frac{6}{7}\right) \). This will give the angle in radians or degrees depending on your calculator settings.
5. Convert the angle to degrees if necessary and round to the nearest whole degree to match one of the given answer choices.