Download 10-6 Polygons

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10-6 Polygons
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(Pages 527–531)
A polygon is a simple, closed figure in a plane that is formed by three
or more line segments, called sides. These segments meet only at their
endpoints, called vertices (plural of vertex). The angles inside the
polygon are interior angles. In a regular polygon, all the interior
angles are congruent and all of the sides are congruent. When a side
of a polygon is extended, it forms an exterior angle. An interior and
exterior angle at a given vertex are supplementary.
Sum of the Interior
Angle Measures
in a Polygon
If a polygon has n sides, then n 2 triangles are formed, and the sum of the degree
measures of the interior angles of the polygon is (n 2)180.
Examples
a. What is the sum of the measures of
the interior angles of a heptagon?
b. What is the measure of each exterior
angle of a regular pentagon?
A heptagon has 7 sides, so let n 7.
(n 2)180 (7 2)180
(5)180 or 900
The sum of the measures of the interior angles
of a heptagon is 900°.
A pentagon has 5 sides, so the sum of the measures
of the interior angles is (5 2)(180) or 540°. Thus,
each interior angle measures 540 5 or 108°.
Each exterior angle measures 180 108 or 72°.
Try These Together
1. Find the sum of the measures of the
interior angles of a triangle.
2. What is the measure of each exterior
angle of a regular hexagon?
HINT: Use the formula and replace n with 3.
HINT: A hexagon has 6 sides.
Practice
Find the sum of the measures of the interior angles of each polygon.
3. octagon
4. 12-gon
5. 18-gon
6. 30-gon
Find the measure of each exterior angle and each interior angle of
each regular polygon. Round to the nearest tenth if necessary.
7. regular triangle
10. regular octagon
8. regular quadrilateral
11. 15-gon
9. regular heptagon
12. 25-gon
Find the perimeter of each regular polygon.
13. regular hexagon with sides 8 cm long
14. regular 17-gon with sides 3 mm long
15. Standardized Test Practice What is the perimeter of a regular octagon if
the length of one side is 12 inches?
A 144 in.
B 96 in.
C 84 in.
D 72 in.
Answers: 1. 180° 2. 60° 3. 1080° 4. 1800° 5. 2880° 6. 5040° 7. 120°; 60° 8. 90°; 90° 9. 51.4°; 128.6° 10. 45°; 135°
11. 24°; 156° 12. 14.4°; 165.6° 13. 48 cm 14. 51 mm 15. B
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Glencoe/McGraw-Hill
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Glencoe Pre-Algebra