Exterior Angles of a Polygon
How to solve the exterior angles of a polygon problems: formula, proof, examples, and their solutions.
The sum of the measures of the exterior angles of an n-gon is 360.
For an n-gon,
there are n of interior angles (purple)
and n of exterior angles (blue).
And there are n of linear pairs. (purple & blue)
Sum of interior angles: 180(n - 2)
Sum of exterior angles: (sum) ← wanted
Sum of the linear pairs: 180n
So 180(n - 2) + (sum) = 180n.
Interior angles of a polygon
The given angles are the exterior angles of a quadrilateral.
So (3x + 40) + (2x + 10) + (120) + (90) = 360.
A regular pentagon has 5 congruent sides
and 5 congruent angles.
So the measure of an exterior angle
of a regular pentagon is 360/5 = 72.
The regular polygon has n congruent sides
and n congruent angles.
And the measure of an interior angle
of the regular polygon is 60.
So 360/n = 60.