Question

question
the figure below shows part of a circle, with central angle as marked. what part of the full circle does the figure represent? express your answer as a
fraction in simplest terms.

Explanation:

Step1: Recall the total degrees in a circle

A full - circle has \(360^{\circ}\).

Step2: Set up the fraction

The fraction of the circle is \(\frac{\text{central angle}}{\text{total degrees in a circle}}\). Given the central angle \(\theta = 80^{\circ}\), the fraction is \(\frac{80}{360}\).

Step3: Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor. The GCD of 80 and 360 is 40. So, \(\frac{80\div40}{360\div40}=\frac{2}{9}\).

Answer:

\(\frac{2}{9}\)