Question

this angle cuts out \\(\frac{2}{9}\\) of the circle. find the measure of the angle. start by writing \\(\frac{2}{9}\\) as a fraction with a denominator of 360. \\(\frac{2}{9} = \frac{\square}{360}\\) so, the measure of the angle is \\(\circ\\).

Explanation:

Step1: Find equivalent fraction

To write $\frac{2}{9}$ with denominator 360, we find what factor we multiply 9 by to get 360. $360\div9 = 40$. So we multiply numerator and denominator by 40: $\frac{2\times40}{9\times40}=\frac{80}{360}$.

Step2: Relate to circle angle

A full circle is $360^\circ$, so the angle measure is the numerator when the fraction of the circle is $\frac{80}{360}$ of $360^\circ$. So the angle measure is $80^\circ$.

Answer:

80