What is the sum of the measures of the exterior angles of a hexagon?
Well I’ve drawn a sketch to help us understand what it’s asking in this question. So now I’ve actually marked on the exterior angles themselves. So we’ve got six exterior angles. And we need to know what the sum of the measures of these exterior angles is.
Well if we actually have a look and bring our exterior angles together, I’ve labeled them one to six, we can see that actually when they’re brought together, they form a circle. And we know that the angles in a circle actually add up to 360 degrees.
So therefore, we can say that the sum of the measures of the exterior angles of our hexagon is equal to 360 degrees. And this isn’t just the case with a hexagon. It’s actually the case for any polygon. The exterior angles will always add up to 360 degrees.
That’s because when we actually bring them together as we did in our diagram, we can actually see that they will form a circle so, therefore, will equal 360 degrees.