Which equation has (2 -1) as a solution

The correct answer is:

n = 5.

Explanation:

On a coordinate grid, an angle starts on the positive x-axis, at 0°.  Multiples of 360° will have their terminal side here as well.

If the terminal side of an angle is on the negative x-axis, this means it is a multiple of 180°.

This gives us 468n° and 180°.  We want the LCM of these two.  To find this, we first find the prime factorization of each number:

468 = 2*234
234 = 2*117
117 = 3*39
39 = 3*13

This gives us:
468 = 2*2*3*3*13
468 = 2²(3²)(13)

We now find the prime factorization of 180:
180 = 2*90
90 = 2*45
45 = 5*9
9 = 3*3

This gives us:
180 = 2*2*3*3*5
180 = 2²(3²)(5)

For the LCM, we multiply the common factors by the uncommon.  The common factors of 468 and 180 are:
2²(3²)

The uncommon factors are:
5*13

This gives us an LCM of:
2²(3²)(5)(13) = 2340

To find the value of n, we solve the equation:
468n = 2340

Divide both sides by 468:
468n/468 = 2340/468
n = 5