Answer:
The measurement of the central angle AOB is 45 degrees
Step-by-step explanation:
To solve this problem, we will have to work with fractions.
We will get the fraction of area the shaded portion is when compared to the whole garden.
First of all, we will need to calculate the area of the garden which is [tex]\pi r^{2}[/tex]
in this case, our radius is 8 inches.
Next, we will compare the area of the sector to the area of the garden. This will be
This will be the shaded area/ area of the whole garden
= [tex]\frac{8\pi}{\pi8^{2}}[/tex]
[tex]=\frac{1}{8}[/tex]
We will now convert this ratio to an angle by multiplying it by 360 degrees.
This will be:
[tex]\frac{1}{8}\times 360 = 45 degrees[/tex]
The measurement of the central angle AOB is 45 degrees
