If an angle is in standard position and its terminal side passes through the point $(1,1)$ on the coordinate plane, what is the measure of the angle in degrees?

• A. $54°$
• B. $117°$
• C. $126°$
• D. $45°$

Answer: (D)

Verified step by step guidance

1. Identify that the angle in standard position has its vertex at the origin (0,0) and its terminal side passes through the point (1,1).
2. Recall that the measure of the angle \( \theta \) can be found using the tangent function, since \( \tan(\theta) = \frac{y}{x} \) for a point \((x,y)\) on the terminal side.
3. Calculate \( \tan(\theta) = \frac{1}{1} = 1 \).
4. Use the inverse tangent function to find the angle: \( \theta = \tan^{-1}(1) \).
5. Recognize that \( \tan^{-1}(1) \) corresponds to an angle of 45 degrees in the first quadrant, so the measure of the angle is \( 45^\circ \).