Answer:
[tex]160^\circ[/tex] is the degrees value of [tex]\theta = \dfrac{8 \pi}{9}[/tex].
Step-by-step explanation:
We are given the following details about the angle [tex]\theta[/tex]:
[tex]\theta =\dfrac{8\pi}{9}\text{ radians}[/tex]
It is know that the relation between radians and degree units is as follows:
[tex]\pi \text{ radians} = 180 ^\circ[/tex]
We can use simply use unitary method to convert radian value of [tex]\theta[/tex] to degrees.
[tex]\pi \text{ radians} = 180 ^\circ[/tex]
[tex]\Rightarrow 1 \text { radian}= \dfrac{\pi}{180} ^\circ[/tex]
[tex]\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[/tex]
Hence, [tex]\theta = 160^\circ[/tex]
