Question

this angle cuts out \\(\frac{2}{9}\\) of the circle. find the measure of the angle. image of a circle with a shaded sector labeled \\(\frac{2}{9}\\) 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 \\(\underline{\quad}\\) °.

Explanation:

Part 1: Rewrite \(\frac{2}{9}\) with denominator 360

Step 1: Find the multiplier

To get from denominator 9 to 360, we calculate \(360\div9 = 40\). So we multiply numerator and denominator by 40.
\(\frac{2}{9}=\frac{2\times40}{9\times40}\)

Step 2: Calculate the numerator

\(2\times40 = 80\), so \(\frac{2}{9}=\frac{80}{360}\)

Step 1: Recall the full - circle angle

A full circle has a central angle of \(360^{\circ}\). If the angle cuts out \(\frac{2}{9}\) of the circle, and we know that \(\frac{2}{9}=\frac{80}{360}\), the measure of the angle is the numerator of the fraction with denominator 360 (since the fraction of the circle corresponds to the fraction of the \(360^{\circ}\) angle).
So the angle measure is \(80^{\circ}\)

Answer:

80

Part 2: Find the angle measure