An angle measuring (468n)° is in standard position. For which value of n will the terminal side fall along the negative portion of the x-axis

since 10*468 = 13*360, if we can find all the values of n < 10, then just adding 10 to those values will produce all the possibilities.

Finding n<10 should not take too long.
For example n=1 works, since 468 = 108(mod 360)

n=5

To determine the value of n for which the terminal side falls along the negative portion of the x-axis, we need to consider the angle in standard position and its degree measurement.

In standard position, the initial side of the angle is the positive x-axis, and the endpoint of the angle, known as the terminal side, determines the direction and position of the angle.

To have the terminal side fall along the negative portion of the x-axis, we need an angle that measures between 180° and 270°, as this region represents the negative x-axis.

Given that the angle measures (468n)°, we need to find the value of n that corresponds to an angle measurement between 180° and 270°.

To do this, we can set up an inequality:

180° < 468n° < 270°

Dividing each term by 468, we have:

180/468 < n < 270/468

Simplifying, we get:

0.384 < n < 0.577

Therefore, the value of n that will make the terminal side fall along the negative portion of the x-axis is any number between 0.384 and 0.577.