Question

this angle cuts out \\(\frac{4}{9}\\) of the circle. find the measure of the angle. image of a circle with a central angle, shaded region labeled \\(\frac{4}{9}\\) start by writing \\(\frac{4}{9}\\) as a fraction with a denominator of 360. \\(\frac{4}{9} = \frac{\square}{360}\\) so, the measure of the angle is \\(\circ\\).

Explanation:

First Sub - Question (Writing \(\frac{4}{9}\) as a fraction with denominator 360)

Step 1: Find the multiplier

To get a denominator of 360 from 9, we calculate \(360\div9 = 40\). So we multiply both the numerator and denominator of \(\frac{4}{9}\) by 40.

Step 2: Calculate the new numerator

Multiply the numerator 4 by 40: \(4\times40=160\). So \(\frac{4}{9}=\frac{160}{360}\).

Step 1: Recall the total degrees in a circle

A full circle has 360 degrees. The angle cuts out \(\frac{4}{9}\) of the circle, and we found that \(\frac{4}{9}=\frac{160}{360}\).

Step 2: Determine the angle measure

Since the fraction of the circle the angle cuts out is \(\frac{160}{360}\), the measure of the angle is 160 degrees (because the measure of the angle in degrees is equal to the numerator when the fraction of the circle is expressed with denominator 360, as a full circle is 360 degrees).

Answer:

160

Second Sub - Question (Finding the measure of the angle)