Question

the diagram shows a regular polygon. what is the value of x? write your answer as an integer or as a decimal rounded to the nearest tenth. x = \boxed{\space}^\circ

Explanation:

Step1: Identify the polygon type

The diagram shows a regular hexagon (6 - sided polygon). For a regular polygon, the measure of an exterior angle \(x\) can be found using the formula for the sum of exterior angles of any polygon, which is \(360^\circ\). The formula for the measure of one exterior angle of a regular \(n\) - sided polygon is \(\frac{360^\circ}{n}\).

Step2: Calculate the exterior angle

For a hexagon, \(n = 6\). Substitute \(n=6\) into the formula \(\frac{360^\circ}{n}\). So, \(x=\frac{360^\circ}{6}\)
\(x = 60^\circ\)

Answer:

\(60\)