The angle subtended at the centre of a circle is \(1\) radian if the length of the arc is equal to the radius of the circle.
\(\text{radians}=\text{degrees}\times \dfrac{\pi}{180^\circ}\)
\(\text{degrees}=\text{radians}\times\dfrac{180^\circ}{\pi}\)
Convert \(120^\circ\) to radians.
\(\begin{aligned} \text{radians}&=120^\circ\times\dfrac{\pi}{180^\circ} \\\\ &=\dfrac{2\pi}{3}\text{ rad} .\end{aligned}\)
Convert \(\dfrac{\pi}{4}\text{ rad}\) to degrees.
\(\begin{aligned} \text{degrees}&=\dfrac{\pi}{4}\text{ rad}\times\dfrac{180^\circ}{\pi} \\\\ &=45^\circ. \end{aligned}\)
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