4. Through what fraction of a circle does the following angle measure? \[ 80^{\circ}= \]

To find the fraction of a circle that an angle measures, we can use the relationship between the angle and the total degrees in a circle. A full circle is \(360^{\circ}\). The fraction of the circle that the angle \(80^{\circ}\) represents can be calculated using the formula: \[ \text{Fraction of circle} = \frac{\text{Angle}}{\text{Total degrees in a circle}} = \frac{80^{\circ}}{360^{\circ}} \] Now, let's simplify this fraction step by step. 1. Write the fraction: \[ \frac{80}{360} \] 2. Find the greatest common divisor (GCD) of 80 and 360. The GCD is 40. 3. Divide both the numerator and the denominator by their GCD: \[ \frac{80 \div 40}{360 \div 40} = \frac{2}{9} \] Thus, the fraction of the circle that the angle \(80^{\circ}\) measures is: \[ \frac{2}{9} \]