Question

this angle cuts out \\(\frac{1}{10}\\) of the circle. find the measure of the angle. start by writing \\(\frac{1}{10}\\) as a fraction with a denominator of 360. \\(\frac{1}{10} = \frac{\square}{360}\\) so, the measure of the angle is \\(\square^\circ\\).

Explanation:

Step1: Find the numerator for denominator 360

To convert $\frac{1}{10}$ to a fraction with denominator 360, we find what number multiplied by 10 gives 360. Let that number be \( x \), so \( 10x = 360 \), then \( x=\frac{360}{10}=36 \). So we multiply numerator and denominator of $\frac{1}{10}$ by 36: $\frac{1\times36}{10\times36}=\frac{36}{360}$.

Step2: Determine the angle measure

A full - circle angle is \( 360^\circ \). If the fraction of the circle the angle cuts out is $\frac{36}{360}$, then the measure of the angle is equal to the numerator of the fraction when the denominator is 360 (since the total degrees in a circle is 360). So the angle measure is \( 36^\circ \).

Answer:

For the fraction: $\frac{1}{10}=\frac{36}{360}$; The measure of the angle is \( 36^\circ \)