an angle measuring (468n)° is in standard position. for which value of n will the terminal side fall on the…

Answer:

B. $n = 5$

Explanation:

Step1: Recall angle - x - axis condition

An angle in standard position has its terminal side on the $x$ - axis if the angle measure is a multiple of $180^{\circ}$, i.e., $(468n)^{\circ}=k\cdot180^{\circ}$, where $k$ is an integer.

Step2: Solve for $n$

We have the equation $468n = 180k$. Simplify the ratio $\frac{468}{180}=\frac{13}{5}$. So, $n=\frac{180k}{468}=\frac{5k}{13}$.

Step3: Find integer value of $k$ for integer $n$

We want to find an integer $k$ such that $n$ is an integer. When $k = 13$, $n=\frac{5\times13}{13}=5$. So when $n = 5$, the angle $(468\times5)^{\circ}=2340^{\circ}$, and $2340\div180 = 13$, which means it is a multiple of $180^{\circ}$ and the terminal - side lies on the $x$ - axis.