6th Grade Math Textbook, Fundamentals

Lesson 9-7 for exercise sets. &KDSWHU 

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Find the sum of the angle measures for each polygon.

1.octagon (8 sides) 2.heptagon (7 sides) 3.11-gon 4.15-gon

Find the value of the variable in each polygon.

7.What is the angle measure of each interior angle of a regular

decagon (a polygon with 10 sides)?

8.What can you say about the relationship of the number of sides of a polygon

and the number of diagonals that can be drawn from each vertex?

9.The sum of the interior angles of a regular n-gon is 1800.

What is the value of n?

10.Discuss and Write Consider any interior angle of a polygon and its

adjacent exterior angle. Why is this pair of angles supplementary?

x

x 142

You can find the sum of any polygon’s interior angle

measures by dividing the polygon into triangles.

number number of

of sides triangles

5  2  3

3 • 180

 540

Key Concept

Measures of Interior Angles of a Regular Polygon

• You can find the measure of each angle in a regular
  polygon using this formula.


• You can use the numerator of this formula to find
  the sum of the angle measures of any polygon.

sum of the angle measures

number of sides of a polygon

(n 2 )• 180

n

Starting from one vertex, draw all possible

diagonals. A is a line segment that

connects two nonadjacent vertices.

Count the number of triangles formed by

the diagonals. This number is two less than

the number of sides.

Multiply the number of triangles by 180.

diagonal

You can use the sum of the interior angle measures of a polygon to find

the measure of a single angle in a regular polygon.

Find the measure of one angle

of a regular pentagon.

Use the formula.

Substitute 5 for n.

Simplify.

3 • 36  108

So in a regular pentagon, each angle measures 108.

3 180

5

36

1

( 5  2 )• 180

5

(n 2 )• 180

n