An angle is drawn in standard position with its terminal side in the second quadrant. Which of the following could be the measure of this angle?

• A. $-180°$
• B. $-120°$
• C. $140°$
• D. $510°$

Answer: (C)

Verified step by step guidance

1. Recall that an angle in standard position has its vertex at the origin and its initial side along the positive x-axis. The terminal side's quadrant depends on the angle's measure.
2. Identify the range of angles that place the terminal side in the second quadrant. The second quadrant corresponds to angles between 90° and 180° when measured counterclockwise from the positive x-axis.
3. Consider that angles can be coterminal, meaning angles differing by full rotations (multiples of 360°) share the same terminal side. So, to check if an angle lies in the second quadrant, find its equivalent angle between 0° and 360° by adding or subtracting multiples of 360°.
4. Apply this to each given angle: for example, for -120°, add 360° to find its positive coterminal angle, then check if it lies between 90° and 180°; repeat this for 140° and 510°.
5. Based on these checks, determine which angles have their terminal side in the second quadrant by verifying if their coterminal angle lies between 90° and 180°.