Question

in circle a, ab = 5 and m∠bac = 144°. find the area of shaded sector. express your answer as a fraction times π.

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{\theta}{360^{\circ}}\times\pi r^{2}\), where \(\theta\) is the central angle of the sector and \(r\) is the radius of the circle.

Step2: Identify the values of \(\theta\) and \(r\)

Given that \(r = AB=5\) and \(\theta = 144^{\circ}\).

Step3: Substitute the values into the formula

Substitute \(r = 5\) and \(\theta=144^{\circ}\) into the formula \(A=\frac{\theta}{360^{\circ}}\times\pi r^{2}\).

$$
LATEXBLOCK0
$$

Answer:

\(10\pi\)