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Section 11.1 – Angle Measures in Polygons
Exercise: In the space below, draw a 3-sided, 4-sided, 5-sided, and 6-sided convex polygon.
On each polygon, choose ONE vertex. Draw all diagonals that connect this vertex with other
vertices in the polygon. This should divide the polygon into triangular regions. Once
completed, fill in the table below.
Polygon
Number of Sides
Number of
Triangles
Sum of Measures of
Interior Angles
Triangle
Quadrilateral
Pentagon
Hexagon
n-gon
Theorems about Interior Angles
Theorem 11.1 “(Polygon) Interior Angle Sum Theorem”: The sum of the measures of
the interior angles of a convex n-gon is _______________________.
Corollary to Theorem 11.1: The measure of each interior angle of a regular n-gon is
___________________________.
Names of Polygons
3 sides = Triangle
4 sides = Quadrilateral
5 sides = _______________________
6 sides = _______________________
7 sides = _______________________
8 sides = _______________________
9 sides = _______________________
10 sides = ______________________
12 sides = ______________________
n sides = _______________________
Examples:
1. What is the sum of the interior angles of a hexagon?
2. How many degrees are there in the sum of the interior angles of a nonagon?
3. If the sum of the interior angles of a polygon equals 900º, how many sides does the
polygon have?
4. What is a polygon called if the sum of its interior angles equals 1440º?
5. Find x in the figure below.
114º
105º
xº
135º
102º
Theorems about Exterior Angles
Theorem 11.2 “(Polygon) Exterior Angle Sum Theorem”: The sum of the measures
of the exterior angles of a convex polygon, one angle at each vertex, is ____________.
Corollary to Theorem 11.2: The measure of each exterior angle of a regular
n-gon is __________________.
Examples:
1.
2yº
yº
yº
2yº
2. Find the measure of the exterior angle of the regular hexagon shown on the right.
xº
3. The measure of each exterior angle of a regular polygon is 40º. How many sides does the
polygon have?
4. Find the value of a.
2aº
3aº
7aº
6aº
2aº