Question

What is the measure of the central angle?
°
What ratio represents the measure of the central angle compared to the measure of the entire circle?

If s = StartFraction theta Over 360 degrees EndFraction (2 pi r), what is the length of minor arc AB?
π

Answer 1

Answer: 140, 7/18, 14

Step-by-step explanation:

Answer 2

The measure of the central angle is 140.

The ratio represents the measure of the central angle compared to the measure of the entire circle is 7/18.

The length of minor arc AB is 14π.

What is the central angle?

A central angle is an angle whose (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B.

For finding the central angle in radians, we have to divide the arc length by the length of the radius of the circle.

1. The measure of the central angle is 140.

2. The ratio represents the measure of the central angle compared to the measure of the entire circle is;

$\rm Ratio=\dfrac{Central \ angle}{Entire \ angle}\\\\ Ratio=\dfrac{140}{360}\\\\Ratio=\dfrac{7}{18}$

The ratio represents the measure of the central angle compared to the measure of the entire circle is 7/18.

3. The length of minor arc AB is;

$\rm Arc \ length =\dfrac{\theta}{360}\times 2\pi r\\\\ Arc \ length =\dfrac{140}{360}\times 2\pi \times 18\\\\ Arc \ length =\dfrac{7}{18}}\times 2\pi \times 18\\\\ Arc \ length =14\pi$

The length of minor arc AB is 14π.

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