Answer: The measure of the central angle indicated in red is 20°
Step-by-step explanation:
We know that a circle subtends an angle of 360° at the centre.
In other words, the circumference of length 6 subtends an angle of 360°, and similarly, we have to find out the angle that length [tex]\frac{1}{3}[/tex] subtends at the centre.
By rule of direct proportion:
if 6→360° Then,
[tex]\frac{1}{3}[/tex] →x°
Cross multiplying
[tex]6x=360*\frac{1}{3}[/tex]
[tex]x=20[/tex]
The general formula for calculating any angle subtended by an arc of length x:[tex]\frac{2*\pi*x }{c}[/tex]
where x is the given length of arc and c is the circumference.
