the measure of central angle ycz is 80 degrees. what is the sum of the areas of the two shaded sectors? 18π…

Explanation:

Step1: Recall sector - area formula

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

Step2: Identify the radius and central - angle measures

The radius of the circle $r = 9$ units. The two shaded sectors have central - angle measures that are vertical angles. Since vertical angles are equal, the sum of the central - angle measures of the two shaded sectors $\theta=80 + 80=160$ degrees.

Step3: Calculate the area of the two shaded sectors

Substitute $\theta = 160$ and $r = 9$ into the sector - area formula: [ \begin{align*} A&=\frac{160}{360}\times\pi\times9^{2}\ &=\frac{4}{9}\times\pi\times81\ &=36\pi \end{align*} ]

Answer:

$36\pi$ units$^{2}$