1. Draw a Diagram and Look for a Pattern
COURSE 2 LESSON 7-6
How many diagonals can be drawn inside a decagon?
The goal is to find the number of diagonals that can be drawn inside a decagon.
Remember that a diagonal is a segment that joins two vertices that are
not endpoints of the same side of a polygon.The diagram below shows
all the diagonals that can be drawn inside each polygon shown.
3 sides 4 sides 5 sides 6 sides
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2. Draw a Diagram and Look for a Pattern
COURSE 2 LESSON 7-6
(continued)
Make a table to organize the information from the diagram.
sides
diagonals 3 4 2 5 6 9
The data in the table indicates that the formula for the number of
diagonals that can be drawn inside a polygon of n sides is
For a decagon, n = 10.
n(n – 3) 2
10(10 – 3)
= = 35
10 • 7
Thirty-five diagonals can be drawn inside a decagon.
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3. Draw a Diagram and Look for a Pattern
COURSE 2 LESSON 7-6
(continued)
To check that 35 diagonals can be
drawn inside a decagon, draw a diagram.
There are 35 diagonals.
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4. Draw a Diagram and Look for a Pattern
COURSE 2 LESSON 7-6
Solve by drawing a diagram and looking for a pattern.
The exterior angles of a triangle are the supplements of the interior angles, as shown. What is the sum of the exterior angles of a
regular hexagon?
360º
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