# For a circle with a diameter of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with o length of 7 3 π meters?

140

Step-by-step explanation:

If it is an arc of 7pi/3, and the circumference is 6*pi or 6pi, then the arc takes up 7/18 of the circle, and since a circle has 360 degrees, the answr is 7/18 * 360 or 140.

Step-by-step explanation:

We know that,

where,

r = radius,

θ = central angle in radian.

Given,

diameter = 6 m, so radius = 3 m.

Putting the values,

Answer : The measurement of a central angle is,

Step-by-step explanation :

Formula used for angle subtended by an arc is:

where,

s = arc length =

r = radius =

Now put all the given values in the above formula, we get:

Thus, the measurement of a central angle is,

The measurement of a central angle (in degrees) subtended by an arc is .

Step-by-step explanation:

as

meters

so

meters

and

meters

Using the formula

Simplify

Therefore, the measurement of a central angle (in degrees) subtended by an arc is .

The measurement of the angle subtended by an arc with a length of 5/2 pi meters is 149.542°

Step-by-step explanation:

Here, the diameter of the circle = 6 m

Diameter = 2 x RADIUS

So, radius = D / 2 = 6 / 2 = 3 m

Also, the length of the arc = ( ) meters

Putting π = 3.14, we get

The length S of the arc =

or, S = 7.85 m

Let us assume the arc subtends angle Ф at the center of the circle.

⇒ S = r Ф

or, Ф =

⇒Ф = 2.61 radians

Now, 1 Radian = 57.2958 Degrees

⇒ 2. 62 Radian = 2.61 x ( 57.2958 Degrees) = 149.542 °

or, Ф = 149.542°

Hence, the measurement of the angle subtended by an arc with a length of 5/2 pi meters is 149.542°

circle circumference = 2 * PI * radius = 2 *PI * 3

18.8495559215

arc length = (7.85381634 / 18.8495559215) * 360 =

0.4166578975 *360 =

150 degrees

C=θ/360πd

thus plugging in the values we get:

5/2π=θ/360π*6

dividing through by 6π we get:

5/12=θ/360

multiplying both sides by 360

θ=150°

diameter=6m

Circumference=pi x d=pi x 6m= 6pi

Circumference/arc length=6pi/(5/2pie)=360degree/central angle

6pie x central angle=360degree x 5/2pie

Central angle=360degree x 5/2pie/6pie

Central angle=360degree x 5/12

Central angle=150degree