Final answer:
The -145° angle lies in Quadrant II, where the x-coordinate is negative and the y-coordinate is positive. The correct answer is option c .
Step-by-step explanation:
The -145° angle lies in Quadrant II. In a coordinate plane, Quadrant II is the upper left quadrant, where the x-coordinate is negative and the y-coordinate is positive.
Angles in a coordinate plane are measured as either positive or negative angles from the positive x-axis. Positive angles are measured counterclockwise and negative angles are measured clockwise. So, a -145° angle is measured clockwise from the positive x-axis.
In Quadrant II, both the x-coordinate and y-coordinate are negative. This means that the angle is in the second quadrant but in the clockwise direction. A -145° angle refers to an angle that is measured 145 degrees in the clockwise direction from the positive x-axis. An angle measured in this manner is considered a negative angle. Normally, when we talk about angles, we start from the positive x-axis and measure counterclockwise for positive angles. Thinking in terms of a full 360-degree rotation, we can determine which quadrant a negative angle lies in by subtracting the negative angle from 360 degrees.
To find the equivalent positive angle for -145°, you calculate 360° - 145° = 215°. This positive angle now lies in the third quadrant (III) because it is greater than 180° but less than 270°. In the Cartesian coordinate system, each quadrant represents a span of 90 degrees, with the first quadrant ranging from 0° to 90°, the second from 90° to 180°, the third from 180° to 270°, and the fourth from 270° to 360°.
Therefore, a -145° angle lies in quadrant III (option c).