Question

Is Pi $\left(\pi \right)$ equal to $180$ degrees.

Answer 1

Checking if $\left(\pi \right)$ equal to $180$ degrees:

Consider a circle of radius $r$

Now draw an arc of length $r$ from the radius.

Join the radius and the arc.

By definition, the angle formed = $1radian$

Full angle = $\theta radians$

Now if $1radian$= $r$,

$\theta radians$ = $2\mathrm{\pi r}$ (circumference)

$$\begin{gathered} \theta \times r=2\mathrm{\pi r} \\ \mathrm{\theta }=2\mathrm{\pi } \\ 360°=2\mathrm{\pi } \\ \mathrm{\pi }=180° \end{gathered}$$

Hence, it is equal to $180$ degrees and $\pi$ radians.