Sum of Exterior angles
- Author:
- Kaela Kunesh, Paul Smith
Part I
Change the angles in different polygons, and then find the sum of the purple exterior angles in each polygon. Record it in your sheet for part I in the chart.
Can you see any pattern? Why might this be the case?
Part II
Let's investigate a triangle below. Interior angles are marked in green. Exterior angles are marked in pink.
d + a =
b + e =
c + f =
Now let's add up all the angles together, interior AND exterior.
a + d + b + e + c + f = ?
So by adding up those angles, you found the sum of interior AND exterior angles in a triangle!
Remember that for any triangle, the sum of interior angles is
Explain why the sum of exterior angles in a triangle must be
Part III
Let's try to show that for ANY polygon, the exterior angles will sum to
In general, remember that our sum of interior angles in an n-gon is
Now consider the sum of interior AND exterior angles.... how could we express the sum of interior and exterior angles for an n-gon?
(hint: remember what we did in part 2. hint 2: consider a quadrilateral)
Use these two pieces of information to show that the sum of exterior angles will always be 360.
Part IV
Let's try to find each exterior angle in a regular polygon.
Measure the exterior angles in the picture by right clicking on it and clicking "show label."
What is the measure of each exterior angle?
Why might this be the case?
How might you find ONE exterior angle in a regular quadrilateral? Explain. (Hint: the sum of exterior angles is 360)
Consider a regular n-gon. How could you find ONE exterior angle for a regular n-gon?