Answer:
72°
Step-by-step explanation:
Given that the radius(r) of the circle is 10 units and the length of arc ABC is 16π
The length of arc ABC = [tex]\frac{\theta}{360}*2\pi r[/tex]
Where θ is the central angle in degrees.
Since the length of arc ABC is 16π,
[tex]16\pi=\frac{\theta}{360}*2\pi r\\16\pi=\frac{\theta}{360}*2\pi *10\\\theta=\frac{16\pi *360}{2 \pi *10} \\\theta=288^0[/tex]
The angle in a circle = 360°, therefore:
Central angle for arc AB (θ) = 360 - Central angle for arc ABC = 360 - 288 = 72°
Therefore the arc measure of arc AB is 72°
