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

Answer:

$\theta=128.5^{\circ}$

Step-by-step explanation:

The given angle measure is

$\theta=\dfrac{257\pi}{360}$

We need to convert the radian measure to degree.

To convert radian to degree, multiply the given measure by $\frac{180^{\circ}}{\pi}$.

$\theta=\dfrac{257\pi}{360}\times \dfrac{180^{\circ}}{\pi}$

On simplification, we get

$\theta=128.5^{\circ}$

Hence, the required measure is $\theta=128.5^{\circ}$.