Given: a convex n-gon
Prove: The sum of the measures of the exterior angles is 360°
Complete the missing parts of the paragraph proof.
For a convex n-gon, interior and exterior angles form
v angles, whose measures sum to 180°.
Because we have an n-gon, the sum of the measures of these linear pairs, one exterior angle at each vertex, is
The sum of the measures of the interior angles is
by the polygon interior angle sum theorem.
To find the measure of the exterior angles, we can subtract the sum of the measures of the interior angles from the
sum of the measures of the linear pairs. Therefore, we have
, which is equal to 360°.
Done