Download 7.5 Angle Relationships in Polygons

7.5
May 20, 2014
Review
Consider the diagram below. Which of the following equations is always true? 7.5 Angle Relationships in Polygons
Learning Goals
• Determine through investigation the properties and relationships of the interior and exterior angles
of polygons.
• Describe the properties and relationships of the interior and exterior angles of polygons.
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May 20, 2014
A polygon is a closed 2D figure with straight sides.
The simplest polygon is a triangle. A quadrilateral is a polygon with four sides.
triangle
quadrilateral
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pentagon
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hexagon
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heptagon
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octagon
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nonagon
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decagon
Investigating the Sum of the Interior Angles of a Polygon
1) Using the quadrilateral on the handout, determine the sum of the interior
angles of the quadrilateral and copy the answer into the chart below.
2) Repeat step 1 for the two other polygons.
Conclusion:
In a polygon with n sides, the sum of the interior angles is
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7.5
May 20, 2014
Investigating the Sum of the Exterior Angles of a Polygon
1) Using the quadrilateral on the handout, extend each side to create exterior angles.
2) Use the fact that an interior angle and its corresponding exterior angle are supplementary
angles to determine the values of the exterior angles.
3) Determine the sum of the exterior angles.
4) Repeat steps 1 to 3 for the two other polygons.
Conclusion:
In a polygon with n sides, the sum of the exterior angles is
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500
500
115
1150
500
0
85
850
0
1150
850
1100
500
850
1150
0
110
1100
1100
Figure 1
Figure 2
Figure 3
Figure 4
If we shrink the quadrilateral, the measure of the exterior angles stays the same.
Eventually the quadrilateral becomes a point, and a complete rotation about a point is 3600.
Example 1) Determine the sum of the interior angles of a 20­sided polygon.
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All regular polygons have equal side lengths and equal interior angles.
Example 2) Determine the measure of an interior angle of a regular hexagon.
Example 3) Each interior angle of a regular polygon is 140o. How many sides does it have?
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May 20, 2014
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