Download You can use what you know about the sum of the interior angle

WS: Interior Angles of Polygons (3.6)
Name _____________________ Pd ____
You can use what you know about the sum of the interior angle measures of a triangle to calculate the
sum of the interior angle measures of a quadrilateral, as well as those of other polygons.
DIAGONAL: A line segment that connects two opposite vertices of a polygon.
1) Draw a quadrilateral with one diagonal.
2) What is the sum of the interior angles of any triangle?
3) In #1, notice that the diagonal divides the quadrilateral into two triangles. If you know the sum of the
measures of the interior angles in each triangle, what is the sum of the measures of the four interior
angles of the quadrilateral? Explain your response.
4) Draw a pentagon. Select ONE vertex and draw all the diagonals that connect to that vertex. Then
complete the table below:
Name of
polygon
Number of
sides
Number of
diagonals from
one vertex
Number of
triangles
formed
Pentagon
1
Sum of
interior angles
in a triangle
Sum of
interior angles
in this polygon
5) Here is a hexagon. Select ONE vertex and draw all of the diagonals that connect to that vertex. Then
complete the table below:
Name of
polygon
Number of
sides
Number of
diagonals from
one vertex
Number of
triangles
formed
Sum of
interior angles
in a triangle
Sum of
interior angles
in this polygon
Hexagon
6) Here is a heptagon. Select ONE vertex and draw all of the diagonals that connect to that vertex. Then
complete the table below:
Name of
polygon
Number of
sides
Number of
diagonals from
one vertex
Number of
triangles
formed
Sum of
interior angles
in a triangle
Sum of
interior angles
in this polygon
7) Here is an octagon. Select ONE vertex and draw all of the diagonals that connect to that vertex. Then
complete the table below:
Name of
polygon
Number of
sides
Number of
diagonals from
one vertex
Number of
triangles
formed
2
Sum of
interior angles
in a triangle
Sum of
interior angles
in this polygon
8) Complete the following table based on your answers to questions 4 – 7.
Name of
polygon
Number of
sides
Number of
diagonals from
one vertex
Number of
triangles
formed
Sum of
interior angles
in a triangle
Sum of
interior angles
in this polygon
Triangle
3
0
1
180°
180°
Quadrilateral
Pentagon
Hexagon
Heptagon
…
…
…
…
…
Octagon
…
…
n
…
…
…
n-gon
…
…
…
…
…
13-gon
21-gon
9) Explain in complete sentences how to calculate the sum of the interior angles in any given polygon.
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A#___ Angles in Polygons
Name _____________________________ Pd _____
Find the sum of the interior angles of the given polygons.
1) Hexagon
2) 15-gon
3) 30-gon
4) Dodecagon
Given the number of sides of a regular polygon, find the measure of each interior angle.
5) 10
6) 6
7) 18
Find the value of x.
8)
9)
10)
Given the measure of each interior angle of a regular polygon, find how many sides the polygon has.
11) 108°
12) 140°
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