Chapter 10.4 Sum of the Interior Angle Measures of a Polygon.notebook
March 05, 2014
Bellwork:
Determine if the following figures are parallelograms, using the stated method.
1. T(­3, ­2), U(­4, 2), X(2, 4), Y(3, 0) ­ slope formula
2. P(2, 3), R(1, ­2), Y(­5, ­7), Z(­4, ­2) ­ distance formula
Solve:
3. 3x ­ 4(x + 3) = ­4
4. ¾(12x ­ 8) = ­15 Mar 5­7:40 AM
Mar 5­10:19 AM
Fill in the # of sides for each polygon.
­ we are going to skip the # of diagonals for the day.
Name of polygon
# of sides
# of diagonals
# of triangles
Sum of angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octogon
Nonagon
Decagon
Hendagon
Dodecagon
N­gon
Mar 5­10:21 AM
Mar 5­7:46 AM
Use the figures on the back of your paper.
­ Draw diagonals from ONE vertex to all non­consecutive vertices.
Name of polygon
# of sides
Triangle
3
Quadrilateral
4
Pentagon
5
Hexagon
6
Heptagon
7
Octogon
8
Nonagon
9
Decagon
10
Hendagon
11
Dodecagon
12
N­gon
n
# of diagonals
# of triangles
Sum of angles
­ Count the #of triangles and fill in the appropriate column
Mar 5­7:51 AM
Mar 5­7:56 AM
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Chapter 10.4 Sum of the Interior Angle Measures of a Polygon.notebook
­ We can fill out the sum of Angles column by starting with the shapes we know, triangles and squares.
­ Use what we know fo triangles to determine the sum of teh angles of a pentagon, a hexagon, and then to find a general formula.
Name of polygon
# of sides
# of diagonals
# of triangles
Name of polygon
# of sides
# of diagonals
March 05, 2014
# of triangles
Sum of angles
Triangle
3
1
180o
Quadrilateral
4
2
360o
Pentagon
5
3
540o
Sum of angles
Triangle
3
1
Quadrilateral
4
2
Hexagon
6
4
720o
Pentagon
5
3
Heptagon
7
5
900o
Hexagon
6
4
Octogon
8
6
1080o
Heptagon
7
5
Octogon
8
6
Nonagon
9
7
1260o
Nonagon
9
7
Decagon
10
8
1440o
Decagon
10
8
Hendagon
11
9
1620o
Hendagon
11
9
Dodecagon
12
10
1800o
Dodecagon
12
10
N­gon
n
n ­ 2
N­gon
n
n ­ 2
180(n­2)o
Mar 5­7:59 AM
Mar 5­8:02 AM
Practice:
Practice:
What is the sum of the interior angles of a 21­sided polygon?
How many sides does a polygon have if the sum of the interior angles are 3780o?
What is the sum of the interior angles of a 14­sided polygon?
How many sides does a polygon have if the sum of the interior angles are 2520o?
What is the sum of the interior angles of a 26­sided figure?
Mar 5­8:07 AM
Regular Polygon: polygon with all equal sides and all equal angles.
How many sides does a polygon have if the sum of the interior angles are 1260o?
Mar 5­8:11 AM
What is the measure of each interior angle of a regular dodecagon?
What is the sum of the interior angles of a dodecagon?
What is another name for a regular triangle?
What is another name for a regular quadrilateral?
Mar 5­8:30 AM
A regular dodecagon has all congruent angles, what can we do to the sum of the interior angles of the dodecagon?
Mar 5­8:33 AM
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Chapter 10.4 Sum of the Interior Angle Measures of a Polygon.notebook
To find the measure of each interior angle of any regular polygon:
­ find the sum of the interior angles and divide by the number of angles (sides)
measure of each interior angle of a regular polygon
March 05, 2014
Practice:
What is the measure of each interior angle of a regular pentagon?
What is the measure of each interior angle of a regular 14­sided polygon?
(n ­ 2) 180
n
Will this work for non­regular polygons?
Mar 5­8:39 AM
How many sides does a regular polygon have that each interior angle measures 120o?
Mar 5­8:43 AM
Practice:
1. PENTA is a regular pentagon. Solve for x.
Homework
10.4 Skills Practice #1­12(odd) and #13­24
2. A convex hexagon has interior angles with measures (4x+4)o, (3x+8)o, 5xo, (6x+4)o, (8x­32)o, and (4x + 14)o.
Mar 5­8:45 AM
Mar 5­9:02 AM
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Mar 5­9:05 AM
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Chapter 10.4 Sum of the Interior Angle Measures of a Polygon.notebook
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March 05, 2014
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