Question

the circle has center o, and the central angle of the shaded sector measures 135°. the area of the shaded sector is what fraction of the area of the circle? (the number of degrees of arc in a circle is 360.)

Explanation:

Step1: Recall the ratio formula

The ratio of the area of a sector to the area of a circle is equal to the ratio of the central - angle of the sector to the total number of degrees in a circle.

Step2: Calculate the fraction

The central angle of the sector is $135^{\circ}$ and the total number of degrees in a circle is $360^{\circ}$. So the fraction is $\frac{135}{360}$.

Step3: Simplify the fraction

$\frac{135\div45}{360\div45}=\frac{3}{8}$

Answer:

$\frac{3}{8}$