Download Section 5.2.notebook

Section 5.2.notebook
November 07, 2011
Lesson 5.2: Angles of Polygons
Shape
Triangle Quadrilateral
Pentagon
Hexagon # of sides
3
4
5 6 # of Triangles
1 2 3 4 What it the pattern from number of sides to # of triangles?
Sides – 2 = Triangles
How many degrees are in one triangle?
Angles Sum Theorem for Polygons
(n – 2)180 = the sum of all angles in a polygon
n = number of sides in the polygon
Sides
3
4
5
6
7
8
Sum of Angles
When a side is added…what gets added to the degrees sum?
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Section 5.2.notebook
November 07, 2011
Examples:
1. Find the sum of the angles of a 12­gon.
2. Find all angles.
2x + 2
2x + 11
4x ­ 2 4x ­ 11
3. A hexagon has two x angles, two (x + 22) angles, and two 90 angles. Find x.
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Section 5.2.notebook
November 07, 2011
Regular Polygon
Each angle of a regular polygon is:
Examples:
4. What are the angles of a regular octagon?
5. If each angle of a regular polygon is 140 , how many sides does the polygon have?
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Section 5.2.notebook
November 07, 2011
6. Does an angle of 173º make a regular polygon?
Exterior Angle Theorem for Polygons
The sum of the exterior angles of a convex polygon is...
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Section 5.2.notebook
November 07, 2011
Exterior Angles of Regular Polygon
What are the degrees of the exterior angles of a regular decagon?
What are the degrees of the interior angles of a regular decagon?
Examples:
7. A heptagon has exterior angles of 90, 48, 54, 72 and the rest of the angles are congruent. What are the missing angles?
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