Question

Convert the angle \theta=\dfrac{8\pi}{9}θ=

Answer 1

Answer:

$160^\circ$ is the degrees value of $\theta = \dfrac{8 \pi}{9}$.

Step-by-step explanation:

We are given the following details about the angle $\theta$:

$\theta =\dfrac{8\pi}{9}\text{ radians}$

It is know that the relation between radians and degree units is as follows:

$\pi \text{ radians} = 180 ^\circ$

We can use simply use unitary method to convert radian value of $\theta$ to degrees.

$\pi \text{ radians} = 180 ^\circ$

$\Rightarrow 1 \text { radian}= \dfrac{\pi}{180} ^\circ$

$\Rightarrow \dfrac{8\pi}{9} \text{ radians} = \dfrac{180}{\pi} \times \dfrac{8\pi}{9} ^\circ\\\Rightarrow \dfrac{180 \times 8}{9}^\circ\\\Rightarrow 20 \times 8^\circ\\\Rightarrow 160 ^\circ$

Hence, $\theta = 160^\circ$