For a circle with a diameter
of 6 meters, what is the measurement of a central angle (in degrees) subtended by an arc with a length of 5/2 pi meters

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°

47 - 90 = 43

43 - 180 = x

x = 137

step-by-step explanation: