Question

Convert the angle \theta=\dfrac{257\pi}{360}θ= 360 257π ​ theta, equals, start fraction, 257, pi, divided by, 360, end fraction radians to degrees. Express your answer exactly. \theta=θ=theta, equals ^\circ ∘

Answer 1

`\theta=128.5^(\circ)`

Explanation:

The given angle measure is

`\theta=(257\pi)/(360)`

We need to convert the radian measure to degree.

To convert radian to degree, multiply the given measure by
`(180^(\circ))/(\pi)`.

`\theta=(257\pi)/(360)* (180^(\circ))/(\pi)`

On simplification, we get

`\theta=128.5^(\circ)`

Hence, the required measure is
`\theta=128.5^(\circ)`.