Question

Is centaral angle of a circle is 360..?

Answer 1

yes
The central angle of a circle is the angle between any two lines drawn from the center of the circle, to it's outer rim. Basically any angle created in the center of the circle (hence the name "central angle"). The circumference of a circle is equal to 2πr (where r is the circle's radius). There are 2π radians in a circle, therefore the central angle in a full circle is equal to 2π. In a unit circle, the radius is of length r=1, therefore the circumference of the circle (aka, the circle's arc length) is equal to 2πr=2π (the circle's central angle). Therefor the circle's central angle, is equal to it's arc length, in the case of a unit circle, where r=1.

This is why mathematicians like to measure angles in units of radians rather than degrees. Once around the circle is 360 degrees but only 2π2π radians.

Moreover, your teacher is talking about a circle whose radius is 11. I hope he or she remembered to mention that.