Question

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

9
8π
​
theta, equals, start fraction, 8, pi, divided by, 9, end fraction radians to degrees.
Express your answer exactly.

Answer 1

160 (pictures for proof)

Explanation:

Answer 2

160°

Explanation:

-Given the angle in radians as
`\theta=(8\pi)/(9)\ rad`

-We know that
`1 \ rad=(180)/(\pi)\textdegree`

-Let our angle theta be X

#We therefore equate and cross multiply:

`1\ rad=(180)/(\pi)\\\\(8\pi)/(9)=x\\\\\therefore X=(180)/(\pi)* (8\pi)/(9)\\\\=160\textdegree`

Hence, angle θ is 160°