Geo­Notes 2­2.notebook
October 08, 2013
Draw a concave pentagon.
Draw a convex irregular heptagon.
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Geo­Notes 2­2.notebook
October 08, 2013
REMEMBER: By the Triangle Sum Theorem, the sum of the interior angle measures of a triangle is 180°.
Using triangles, what's the sum of the interior angles of each figure?
What do you notice?
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Geo­Notes 2­2.notebook
October 08, 2013
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Geo­Notes 2­2.notebook
Number of Number of sides
triangles
October 08, 2013
Sum of Interior Angles
Measure of one interior angle (Regular Polygon
only)
n
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Geo­Notes 2­2.notebook
October 08, 2013
Theorem 2-3
Polygon Interior Angle-Sum Theorem
The sum of the interior angle measures of
a convex polygon with n sides is (n - 2) 180°.
http://www.mathopenref.com/polygoninteriorangles.html
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Geo­Notes 2­2.notebook
October 08, 2013
1. Find the sum of the interior angle measures of a...
convex heptagon.
regular 16­gon.
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Geo­Notes 2­2.notebook
October 08, 2013
In a regular polygon with n sides
the measure of one interior angle is
(n - 2)180
n
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Geo­Notes 2­2.notebook
October 08, 2013
2. What is each measure of the interior angle of a regular 18­gon?
What is each interior angle of a dodecogon? 8
Geo­Notes 2­2.notebook
October 08, 2013
3. Find the measure of the
missing angle of the quadrilateral.
91°
79°
x
125°
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Geo­Notes 2­2.notebook
October 08, 2013
In the polygons below, an exterior angle has been measured at each vertex. Notice that in each case, the sum of the exterior angle measures is 360°.
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Geo­Notes 2­2.notebook
October 08, 2013
Exterior Angles
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Geo­Notes 2­2.notebook
October 08, 2013
Theorem 2-4
Polygon Exterior Angle-Sum Theorem
The sum of the measures of the
exterior angles of a polygon, one at
each vertex, is 360°.
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Geo­Notes 2­2.notebook
October 08, 2013
4. Find the measure of each exterior angle of a regular 20­gon.
NOTE: One exterior angle of a regular polygon with n
sides = 360
n
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Geo­Notes 2­2.notebook
October 08, 2013
5. Find the value of b in polygon FGHJKL. 14
Geo­Notes 2­2.notebook
October 08, 2013
6. Ann is making paper stars for party decorations. What is the measure of ∠1?
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Geo­Notes 2­2.notebook
October 08, 2013
7. Find the measure of each interior angle of pentagon ABCDE. You will have to find the value of c.
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Geo­Notes 2­2.notebook
October 08, 2013
8. The measure of an exterior
angle of a regular polygon is 60°.
Find the number of sides.
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Geo­Notes 2­2.notebook
October 08, 2013
HW # 20
p. 79­80 # 1­4,10­17,19­26
Quiz on Friday !!!!
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