As you know, the length of an entire circumference of a radius `r` is `2 pi r,` and an entire circumference contains the central angle of 360 degrees.
Also the length of an arc is proportional to the measure of its central angle. The proportion is:
length of an arc with an angle `alpha` : length of an entire circumference = `alpha` : 360°,
length for angle alpha : `2 pi r` = `alpha` : 360°
(alpha is in degrees also).
Thus the length is `2 pi r * alpha/360,` in our case it is `(2 pi *10*50)/360=pi*25/9,` or approximately `8.73.`