Sum of the Interior Angles of a
Polygon
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Printed: July 21, 2012
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C ONCEPT
1
1
Sum of the Interior Angles of
a Polygon
Lesson Plan
Launch (20 min)
• Guide the students by answering # 1 and completing the table for the first two rows (triangle and quadrilateral).
Confusion on the diagonals from one vertex may still exist. Help setup the diagonals in the pentagon if
necessary.
• Students complete the rest of the activity individually.
Presentation (20 min)
• (5 min) Debrief the launch by asking for patterns. See if students were able to come up with the equation on
their own. Use this as the springboard into the presentation.
• (15 min) Sum of the interior angles of a polygons = (n − 2) ∗ 180 where n = of sides
– Teach examples 1 and 2.
Practice (15 min)
• Students work through the problems on their own
• The most common mistake will be when students look for the interior angle measure of a regular polygon they
will divide by (n − 2) instead of n.
Conclusion (10 min)
• Write how to solve the problem. Swap and peer edit responses for strength of explanation/solution.
Exit Ticket (5 min)
Materials
Rulers
Lesson Packets
Launch
Breaking it down...
1. What do we know about the sum of the interior angles of a triangle? ____________.
INSTRUCTIONS: Since we know the sum of the interior angles of a triangle, construct diagonals from one vertex
to all remaining vertices to construct triangles. Also, name the polygon based on sides.
Concept 1. Sum of the Interior Angles of a Polygon
2
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Complete the table below using the triangles you just created and try and formulate a rule for the sum of the interior
angles of a polygon.
TABLE 1.1:
Convex Polygon
Number of Sides
Number of Triangles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
N−gon
∗ What
would the sum of the interior angles of a 100-gon be?∗
Presentation
Ex 1: Find the sum of the interior angles of a hexagon.
... what is the measure of each angle of a regular hexagon?
Sum of the triangles
Rule?
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3
TABLE 1.2:
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
n−gon
# of sides
Ex 2: Find the sum of the interior angles of a decagon.
-What is the measure of each angle of a regular decagon?
Practice
Instructions: Find the measure of the sum of the interior angles of the indicated polygon. SHOW ALL WORK.
1. Nonagon
2. 14-gon
3. 16-gon
Instructions: Find the measure of EACH angle of the REGULAR polygons. Show all work.
4. 20-gon
5. Pentagon
6. Octagon
Instructions: Find the value of x.
7.
8.
Concept 1. Sum of the Interior Angles of a Polygon
4
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9.
a=
b=
10.
a=
b=
c=
d=
e=
f=
g=
h=
i=
j=
Conclusion
A tridecagon is a polygon with 13 sides. Explain how you could find the measure of each angle of a regular
tridecagon.
Justify your answer. You must use at least 4 words from the word bank and write at least 3 complete sentences .
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5
Homework
Directions: Find the area and perimeter of the regular polygons.
1. What is the sum of measures of the interior angles of a 5-sided polygon (pentagon)?
a) Sketch a picture of the pentagon and use triangles to find the sum.
b) Use the formula 180 ∗ (n − 2) to find the sum.
2. What is the sum of measures of the interior angles of a 15 sided polygon?
3. If the polygon in number 2 were a regular polygon, what would be the measure of each angle?
4. Find the value of x in the polygon shown.
5. Explain (in complete sentences) where the (n − 2) comes from in the formula to find the sum of the measures of
the interior angles of an n−sided polygon, 180 ∗ (n − 2).
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Concept 1. Sum of the Interior Angles of a Polygon
6
Exit Ticket
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