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

Answer:

Therefore,

The Central Angle is 48°.

Step-by-step explanation:

Given:

Circumference = 12 units

$Arc\ length = \dfrac{8}{5}= 1.6\ unit$

To Find:

Central angle = θ = ?

Solution:

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

$Arc\ length = \dfrac{\theta}{360}\times Circumference$

Substituting the values we get

$1.6 = \dfrac{\theta}{360}\times 12\\\\\theta = 48\°$

Therefore,

The Central Angle is 48°.

Answer 2

Since the circumference of this circle is 12 units, the central angle that is subtended by the arc is equal to 18.75 degrees.

Given the following data:

• Cirumference = 12 units.

• Arc length = 8/5.

How to calculate the central angle of the arc?

In Mathematics, if you want to calculate the central angle that is formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.

Mathematically, the arc length formed by a circle is given by:

Arc length = C × θ/360

5/8 = 12 × θ/360

5/8 = 12θ/360

5/8 = θ/30

θ = 150/8

Central angle = 18.75 degrees.

Read more on circumference here: brainly.com/question/14478195