Question

use the drop - down menus to complete the sentences: the terminal ray of an angle measuring $-\frac{10}{9}pi$ lies in the quadrant. this angle measures °.

Explanation:

Step1: Convert radians to degrees

We know that to convert radians to degrees, we use the formula $D = R\times\frac{180^{\circ}}{\pi}$, where $D$ is the degree - measure and $R$ is the radian - measure. Given $R =-\frac{10}{9}\pi$. Then $D=-\frac{10}{9}\pi\times\frac{180^{\circ}}{\pi}=- 200^{\circ}$.

Step2: Determine the quadrant

To find the quadrant of an angle, we add $360^{\circ}$ to the negative angle to get it in the range of $0^{\circ}$ to $360^{\circ}$. $-200^{\circ}+360^{\circ} = 160^{\circ}$. Since $90^{\circ}<160^{\circ}<180^{\circ}$, the angle lies in the second quadrant.

Answer:

The terminal ray of an angle measuring $-\frac{10}{9}\pi$ lies in the second quadrant. This angle measures $-200^{\circ}$.