Question

the measures of two angles in standard position are given. determine whether the angles are coterminal. -210°, 150° the angles are coterminal. the angles are not coterminal.

Explanation:

Step1: Recall coterminal - angle formula

Two angles $\alpha$ and $\beta$ are coterminal if $\alpha-\beta = 360^{\circ}n$, where $n$ is an integer. Let $\alpha = 150^{\circ}$ and $\beta=- 210^{\circ}$. Then calculate $\alpha - \beta$.

Step2: Calculate the difference

$\alpha-\beta=150^{\circ}-(-210^{\circ})=150^{\circ}+210^{\circ}=360^{\circ}$. Since $360^{\circ}=360^{\circ}\times1$ and $1$ is an integer.

Answer:

The angles are coterminal.