Download Geometry Notes G.10 (8.1) Polygons Mrs. Grieser Name: Date

Geometry Notes G.10 (8.1) Polygons
Mrs. Grieser
Name: _______________________________ Date: _____________ Block: _______
Polygons

Polygons: simple, closed figure formed by 3 or more coplanar line segments (sides); sides
meet at endpoints (vertices - singular: vertex)

Concave vs. Convex:
o concave polygons contain a reflex angle (greater than 180o);
o convex do not!

Circle the concave polygons; put a box around the convex polygons
Not
Polygons:
Polygons:

Regular Polygons: equilateral and equiangular

Diagonal: line segment that joins two nonconsecutive vertices
Polygon Interior Angles Theorem
The sum of the measures of the interior angles of a convex n-gon is (n-2)∙180
m<1 + m<2 + … + m<n = (n-2)∙180
Corollary:
The sum of the measures of the interior angles of a quadrilateral is 360o.

Find the measure of an interior angle of a regular polygon with n sides
o Measure of the sum of interior angles: ____________
o Each angle in a regular polygon is __________
o  the measure of an interior angle of a regular polygon with n sides is _________
Polygon External Angles Theorem
The sum of the measures of the exterior angles of a convex polygon, one
angle at each vertex, is 360o.

Find the measure of an exterior angle of a regular polygon with n sides
o Measure of the sum of exterior angles: ____________
o Each angle in a regular polygon is __________
o  the measure of an exterior angle of a regular polygon with n sides is _________
o In a regular convex polygon, an interior angle = 180 – measure of exterior angle
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Geometry Notes G.10 (8.1) Polygons
Examples:
Mrs. Grieser
a) Find the sum of the measures of the
interior angles of a convex octagon.
b) The sum of the measures of the interior
angles of a convex polygon is 900o.
Classify the polygon by the number of sides.
c) Find x.
d) Find x.
You Try:
a) Find the sum of the measures of the
interior of a convex hexagon.
b) The sum of the measures of the interior
c) Find x.
d) A convex heptagon has exterior angles with
measures 60o, 51o, 67o, 48o, 32o, and 59o.
What is the measure of an exterior angle
at the seventh vertex?
e) What is the measure of an interior angle of
a regular nonagon?
f) What is the measure of an exterior angle
of a regular dodecagon?
g) Find x.
h) Find n if each interior angle of a regular n-gon
measures 172.8.
angles of a convex polygon is 2700o.
Classify the polygon by the number of sides.
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