Answer: 304.6°
Explanation:
First of all, using the circumference of the circle formula to find the radius of the circle.
Circumference of the circle = 13, ie
2πr = 13,
r = 13/2π ---------------------------- 1
Now getting the radius of the circle now, you now substitute for this in the formula for finding the length of an arc to get the central angle.
Arc length = 11 , ( 2πr0°/360) or (πr0°/180), so
πr0°/180 = 11 ------------------------ 2
Now solve for 0°, the central angle of the angle by making it the subject of the formula.
πr0° = 180 x 11
0° = 180 x 11
----------- ----------------- 3
πr
Now, put equation 1 in equation 3 and solve.
0° = 1980
--------
π x 13/2π
= 1980 x 2π
-----------
π.x. 13
= 1980 x 2
----------
13
= 3960/13
= 304.6°
Therefore, the central angle of the arc is 304.6°
Please be meticulous and understand the way I change the r in the denominator. It was the rule in fraction when dividing.