Download Lesson 3: Properties of Polygons

U3 D3 Angle Relationships in Polygons.notebook
March 03, 2017
Key Terms
Unit 3 ­ Geometric Relationships
Day 3 ­ Angle Relationships in Polygons
• Although triangles and quadrilaterals are common, we may need to deal with other polygons.
• Polygon: A 2D closed figure whose sides are line segments. • Regular polygon: All sides are equal and all interior angles are the same
Learning Goals
Today, we will learn...
• How to calculate the unknown measure(s) of interior angles and exterior angles of different polygons
• How to tell how many sides are in a polygon given the sum of the interior angles
Sep 21­10:01 AM
• Convex polygons have interior angles that measure less than 1800.
• Concave polygons can have interior angles greater than 1800.
Feb 4­3:41 PM
Let's Investigate
Create and complete the following chart:
POLYGON NAME # OF SIDES
# OF TRIANGLES
SUM OF SUM INTERIOR EXTERIOR ANGLES
ANGLES TRIANGLE
Conclusion: the sum of interior angles of a polygon is:
QUADRILATERAL
The sum of exterior angles of any polygon is PENTAGON
HEXAGON
HEPTAGON
Mar 3­8:34 AM
Mar 3­8:39 AM
Practice
Example 1: A garden pond is built in the shape of a regular polygon with 15 sides. Find the measure of each of the exterior angles. Example 2: a) A patio is made in the shape of a regular polygon with 24 sides. Find the sum of the interior angles. b) Find the measure of each of the interior angles of the patio in part a). Feb 4­3:51 PM
Feb 4­3:51 PM
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U3 D3 Angle Relationships in Polygons.notebook
March 03, 2017
Example 3: The sum of the interior angles of a polygon is 2700º. Find the number of sides. Example 4: Determine the number of sides in a regular poygon if each exterior angle is 40
Feb 27­7:53 AM
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