Question

this angle cuts out \\( \frac{1}{2} \\) of the circle. find the measure of the angle. start by writing \\( \frac{1}{2} \\) as a fraction with a denominator of 360. \\( \frac{1}{2} = \frac{\square}{360} \\) so, the measure of the angle is \\( \square \\). (accompanied by an image of a circle with a semicircular region shaded, labeled \\( \frac{1}{2} \\))

Explanation:

Step1: Convert fraction to 360 denominator

To write \(\frac{1}{2}\) with denominator 360, we find what number we multiply 2 by to get 360. Since \(360\div2 = 180\), we multiply numerator and denominator by 180: \(\frac{1\times180}{2\times180}=\frac{180}{360}\)

Step2: Determine angle measure

A full circle is \(360^\circ\), so the fraction of the circle the angle cuts out is \(\frac{180}{360}\), meaning the angle measure is \(180^\circ\) (because the measure of the angle is the fraction of the circle times \(360^\circ\), so \(\frac{180}{360}\times360 = 180\))

Answer:

First blank: 180; Angle measure: \(180^\circ\)