Why Pi radian is 180 degrees

We always heard that in radians the value of pi is 180 degrees. That is not quite right. Let’s understand this by finding the origin of radians.

Let’s say we have a circle of radius r. We cut an arc of which is of radius r. Then the produced angle is said to be 1 radian which is denoted as 1ᶜ. If we multiply the value of π with 1ᶜ, the line will be a straight line. The value of the angle of a straight line in degree measurements is 180 degrees. This is why if we convert the value π from radians to degree the value will be 180. We were taught usually that the value of π in radian is 180 and in degree 3.1416 which is not correct conceptually and verbally. Actually, π is always 3.1416 where if we convert the value of π radians or 3.1416 radians in degree it is 180.

Mathematically explanation:

If arc, radius and angle is expressed as s, r and θ simultaneously,
we know, s = rθ;
If C is the circumference then
C = 360° r [where s= C and θ = 360°]
or 2πr = 360° r
or π = 180°