Regular Polygons and Angle Relationships
Regular Polygons and Angle Relationships
Regular Polygons and Angle Relationships
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<strong>Regular</strong> <strong>Polygons</strong> <strong>and</strong> <strong>Angle</strong> <strong>Relationships</strong> (pp. 4 of 7)<br />
Geometry<br />
HS Mathematics<br />
Unit: 12 Lesson: 01<br />
17. Repeat the procedure to find the measure of each of the interior <strong>and</strong> exterior angles of a<br />
regular pentagon, regular hexagon, regular heptagon, <strong>and</strong> regular octagon as well as the<br />
exterior angle sum. Record your data in the table below.<br />
Polygon<br />
Name<br />
Number of<br />
Sides, n<br />
Sum of the<br />
Interior<br />
<strong>Angle</strong>s<br />
(n – 2)180<br />
Triangle 3 180<br />
Quadrilateral<br />
Pentagon<br />
Hexagon<br />
Heptagon<br />
Octagon<br />
n-gon<br />
Process to<br />
Find the<br />
Measure of<br />
an Interior<br />
<strong>Angle</strong><br />
Measure of<br />
Each Interior<br />
<strong>Angle</strong><br />
Measure of<br />
Each Exterior<br />
<strong>Angle</strong><br />
Exterior<br />
<strong>Angle</strong> Sum<br />
(one angle<br />
at each<br />
vertex)<br />
a. Describe the process for finding the measure of an interior angle of a regular polygon.<br />
b. Describe the process for finding the measure of an exterior angle of a regular polygon.<br />
c. Based on the data in the table, describe how the measure of an interior angle changes as<br />
the number of sides of the regular polygon changes. What does this lead you to believe<br />
about the relationship between the measure of an interior angle of a polygon <strong>and</strong> the<br />
number of sides of a regular polygon?<br />
© 2008, TESCCC 12/03/08 page 24 of 49
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