An arc of length 28cm subtends an angle of 24 at the centre of a circle in the same circle. what angle does an arc of length 35cm subtend?

Answer 1

We can use the formula for the relationship between the central angle, the arc length, and the circumference of a circle:

angle = (arc length / circumference) x 360 degrees

Let C be the circumference of the circle. Then we have:

24 degrees = (28 cm / C) x 360 degrees

Solving for C, we get:

C = (28 cm / 24 degrees) x (360 degrees / 1) = 420 cm

Now we can use the same formula to find the angle for an arc of length 35 cm:

angle = (35 cm / 420 cm) x 360 degrees = 30 degrees

Therefore, an arc of length 35 cm subtends an angle of 30 degrees at the centre of the circle.