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Honors Geometry
Unit 4C
Name________________
Date________________
Regular Polygon Practice
The outer shape is a regular pentagon. Find the measures of the five angles
indicated in the diagram.
1
2
5
3
4


m 1  __________
m 2  __________
m 4  __________
m 5  __________
RegPolyPrac.doc



m 3  __________
Mr. John Cendrowski
Lower Moreland HS
Honors Geometry
Unit 4C
Page 2
The outer shape is a regular octagon, the middle shape is a regular pentagon,
and the inner shape is a regular triangle. Find the measures of the five angles
indicated in the diagram.
1
5
4
3
2


m 1  __________
m 2  __________
m 4  __________
m 5  __________
RegPolyPrac.doc



m 3  __________
Mr. John Cendrowski
Lower Moreland HS
Honors Geometry
Unit 4C
Page 3
Using the formulas
1.
How many sides does a regular polygon have if the sum of the interior
angles is 3420˚?
2.
How many sides does a regular polygon have if the number of diagonals
that can be drawn is 35?
3.
How many sides does a regular polygon have if the measure of each
exterior angle is 20?
4.
How many diagonals does a regular hexagon have?
5.
What is the sum of the measures of the interior angles of a regular
22-gon?
6.
What is the measure of each interior angle of a regular 20-gon?
7.
What is the measure of each exterior angle of a regular 24-gon?
RegPolyPrac.doc
Mr. John Cendrowski
Lower Moreland HS
Honors Geometry
Unit 4C
Page 4
Going Beyond
1.
How many more degrees are in the exterior angle of a regular polygon
with 10 sides than one with 15 sides?
2.
A rectangle with sides 6 and 4 has the same area as a square. Find the
perimeter of the square.
3.
A regular dodecagon has 12 sides. What is the measure of a central
angle in this figure? What is the measure of an exterior angle of this
figure?
4.
A regular polygon has 44 diagonals. How many sides does the shape
have?
5.
An equilateral triangle is placed on top of a square of area 20 m2 as
shown in the figure below. Find the perimeter of the shape.
6.
A regular pentagon and a square share a mutual vertex X . The sides
XY and XZ are sides of a third regular polygon with a vertex at X . How
many sides does this third polygon have?

Y



X
Z
RegPolyPrac.doc
Mr. John Cendrowski
Lower Moreland HS
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