Question

A circle has a circumference of \blue{12}12start color #6495ed, 12, end color #6495ed. It has an arc of length \dfrac{8}{5} 5 8 ​ start fraction, 8, divided by, 5, end fraction. What is the central angle of the arc, in degrees? ^\circ ∘ degrees

Answer 1

To find the central angle of an arc with a length of 8/5 in a circle with a circumference of 12, we set up a proportion with the full circle's 360 degrees and solve for the angle, resulting in a central angle of 48 degrees.

Step-by-step explanation:

You want to find the central angle of an arc in degrees for a circle with a circumference of 12 units and an arc length of 8/5 units. Since the circumference of a circle is 2π times the radius (2πr) and corresponds to a full circle or 360 degrees, the angle for the entire circle is 360°. The arc length of 8/5 is a fraction of the total circumference, so to find the corresponding angle in degrees, set up the proportion:

(arc length) / (circumference) = (angle of arc) / (360 degrees)

Plug in the known values and solve for the angle of the arc:

(8/5) / 12 = (angle) / 360

Cross-multiply to solve for the angle:

360 * (8/5) = 12 * (angle)

angle = (360 * 8) / (5 * 12)

angle = 48 degrees

Therefore, the central angle of the arc is 48 degrees.

Answer 2

Therefore,

The Central Angle is 48°.

Step-by-step explanation:

Given:

Circumference = 12 units

`Arc\ length = (8)/(5)= 1.6\ unit`

To Find:

Central angle = θ = ?

Solution:

If "θ" the central angle is in degree then arc of length is given by

`Arc\ length = (\theta)/(360)* Circumference`

Substituting the values we get

`1.6 = (\theta)/(360)* 12\\\\\theta = 48\°`

Therefore,

The Central Angle is 48°.