Angles of
Polygons
Polygon Interior Angle Theorem
The sum of the measures of the interior
angles of a convex polygon is given by:
Sum = 180(n – 2)
where n represents the number of sides in
the polygon
Polygon Interior Angle
Theorem
 Find
the sum of the measures of the
interior angles of an octagon
Interior Angle of a Polygon
 The
find a single interior angle:
Measure of Interior Angle =
Interior Angle Sum
n number of sides
Interior Angle of a Polygon
 If
a regular polygon has 14 sides, what is
the measure of one of the interior angles?
Exterior Angles of a Polygon
Polygon Exterior Angle Theorem
The sum of the measures of the exterior
angles of a convex polygon, one angle at
each vertex, is 360°.
Exterior Angles of a Polygon
 What
is the sum of the measures of the
exterior angles of a heptagon?
 What
is the sum of the measures of the
exterior angles of a polygon with 324
sides?
Exterior Angle of a Polygon
To find a single exterior angle:
Exterior angle sum
n number of sides
Exterior Angle of a Polygon
 Find
the measure of an exterior angle of a
regular nonagon.
 If
an interior angle of a regular polygon
measures 108°, how many sides does the
polygon have?
Practice
 P.368:
3-30