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11.1 Angle Measures in Polygons
Geometry
Polygon Angle Measures
Polygon
TRIANGLE
QUADRILATERAL
PENTAGON
HEXAGON
…..
N-GON
# of sides
# of congruent
triangles
Sum of measures of
interior angles
POLYGON INTERIOR ANGLES THEOREM
The sum of the measures of the interior
angles of a convex n-gon is…
(n – 2) · 180
Regular Polygons
What is the difference between a polygon and a
regular polygon?
More Regular Polygons
COROLLARY TO THEOREM 11.1
Example
Example
Find the value of x in the diagram.
114°
105°
x°
135°
102°
Example
The measure of each interior angle of a regular
polygon is 140°. How many sides does the
polygon have?
Example
The measure of each interior angle of a
regular polygon is 165 degrees. How many
sides does the polygon have?
Examples
1. A heptagon has four interior angles that
measure 160 degrees each and two interior
angles that are right angles. What is the
measure of the other interior angle?
2. Find the measure of each angle in a regular
11-gon.
Interior vs Exterior
Exterior Angles
Walk around the polygon
POLYGON EXTERIOR ANGLES
THEOREM
The sum of the measures of the exterior
angles of a convex polygon, one angle at each
vertex, is 360.
COROLLARY TO THEOREM 11.2
Example
Find x
Example
The measure of each exterior angle of a
regular polygon is 40 degrees. How many
sides does the polygon have?
Example
The sign on a building has a long narrow
hexagon shape. Four of the interior angles
measure 140 degrees each. The remaining
two interior angles at each end of the sign are
congruent. What is the measure of each
angle.
Example
If you were designing a sign for a new
building, would it be possible to make a sign
that is a regular polygon with each angle
having a measure of….
a. 160 degrees
b. 115 degrees