Question

Find the measure of each of the exterior angles of the regular hexagon using the Polygon Exterior Angle Sum Theorem.

Answer 1

$60^{\circ}$

1) Given that this hexagon is a convex polygon, then we can tell that the sum of those exterior angles is equal to 360º

2) Since this is a regular hexagon, then all their 6 sides measure the same and therefore their exterior angles have the same measure.

3) Thus, we can write out the following equation:

$\begin{gathered} m\angle1\cong m\angle2\cong m\angle3\cong m\angle4\cong m\angle5\cong m\angle6=x \\ 6x=360 \\ \frac{6x}{6}=\frac{360}{6} \\ x=60 \end{gathered}$