Question

in circle e above, arc fhg is 45 cm long. the circumference of the circle is 112.5 cm. what is the measure of the central angle?
a. 60°
b. 180°
c. 360°
d. 144°

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) is \(s=\frac{n}{360}\times C\), where \(n\) is the measure of the central angle in degrees and \(C\) is the circumference of the circle.
We are given that \(s = 45\) cm and \(C=112.5\) cm.

Step2: Solve for \(n\)

Substitute the given values into the formula \(s=\frac{n}{360}\times C\).
We get \(45=\frac{n}{360}\times112.5\).
First, rewrite the equation as \(n=\frac{45\times360}{112.5}\).
Calculate \(45\times360 = 16200\).
Then \(n=\frac{16200}{112.5}=144\).

Answer:

D. \(144^{\circ}\)