Question

N circle o, radius oq measures 9 inches and arc pq measures 6π inches. what is the measure, in radians, of central angle poq? 2pi/3 radians 3pi/4 centimeters 4pi/3 radians 3pi/2 radians

Answer 1

 θ = 6π/9 =  2π/3  radians

Answer 2

Answer: $\frac{2\pi}{3}$ radians

Step-by-step explanation:

Given: In circle O, the radius of circle = 9 inches

The arc length of PQ= $6\pi$ inches

Let $\theta$ be the measure of the angle .

The formula to calculate arc length(l) for radius r and angle x is given by :-

$l=r*\x\\\\\Rightarrow\ x=\frac{l}{r}$

According to the question we have,

$\theta=\frac{6\pi}{9}=\frac{2\pi}{3}$

Hence, the measure, of central angle POQ= $\frac{2\pi}{3}$ radians