Question

the measure of angle g is $\frac{pi}{10}$ radians. if the measure of angle g is 9n degrees, where n is a constant, what is the value of n? a 2 b 9 c 10 d 18

Explanation:

Step1: Recall conversion formula

We know that to convert from radians to degrees, we use the formula $1$ radian $=\frac{180^{\circ}}{\pi}$. So, if an angle $\theta$ is $\frac{\pi}{10}$ radians, in degrees it is $\theta_d=\frac{\pi}{10}\times\frac{180^{\circ}}{\pi}$.

Step2: Simplify the expression

$\frac{\pi}{10}\times\frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{10} = 18^{\circ}$.
Since the measure of angle $G$ is also $9n$ degrees and it is equal to $18^{\circ}$, we set up the equation $9n = 18$.

Step3: Solve for $n$

Dividing both sides of the equation $9n = 18$ by $9$, we get $n=\frac{18}{9}=2$.

Answer:

A. 2