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

The angle is 1560°

Step-by-step explanation:

The length of an arc in radian is given by s=rФ

where s=length of an arc, r=radius and Ф = angle in radians

The question asked us to find the angle

Given to us is; r =6m and s=52π  and Фis what we are to find

From the formula s= rФ

Ф= s/r   =  52πm/6m

Ф=52π/6

Ф=26π/3 radians

But the question states that the angle should be in degree, so we will change the above angle to degree, to do that we will simply multiply the angle by 180°/π

Thus;

Ф=26π/ 3   ×    180°/π

(The π at the numerator will cancel that of the denominator, and 180° will be divided by 3 to give 60°, we will be  left with just 26 and 60 at the numerator)

Ф = 26× 60°

Ф=1560°

Therefore, the central angle (in degree) subtended by an arc with length 52πmeters and radius 6 meters is  1560°

m∠a is 90°

m∠b is 40°