Question

example #1: draw an angle with the given measure in standard position.
a. 240°

Explanation:

Step1: Identify quadrant for 240°

A standard position angle has its vertex at the origin, initial side along the positive x-axis. Since $180^\circ < 240^\circ < 270^\circ$, the angle lies in Quadrant III.

Step2: Calculate reference angle

$240^\circ - 180^\circ = 60^\circ$
This means the terminal side is $60^\circ$ below the negative x-axis.

Step3: Plot the angle

1. Start with the initial side on the positive x-axis.
2. Rotate counterclockwise $240^\circ$ (or rotate $180^\circ$ to the negative x-axis, then an additional $60^\circ$ downward into Quadrant III) to draw the terminal side.

Answer:

An angle in standard position with measure $240^\circ$ has its vertex at the origin, initial side along the positive x-axis, and terminal side in Quadrant III, $60^\circ$ below the negative x-axis (as described in the plotting steps).

(Visual representation: On the given x-y axes, draw a ray starting at the origin, rotated 240 degrees counterclockwise from the positive x-axis, landing in the third quadrant.)