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Angle Relationships in Polygons April 24, 2013 What's Going On? The Last Test Polygon Investigation Angle Relationships in Polygons Aquayo! Learning Goal I will be able to determine and describe the properties and relationships of the interior and exterior angles of polygons. 1 Angle Relationships in Polygons April 24, 2013 Exit Question from Last Time Find the measure of angles w, x, y and z. JUSTIFY w x y z 59o 2 Angle Relationships in Polygons April 24, 2013 Aquayo! 3 Angle Relationships in Polygons April 24, 2013 Unit 6: Geometric Relationships Topic #3 Angle Relationships in Polygons 4 Angle Relationships in Polygons April 24, 2013 A New Term Regular Polygons 5 Angle Relationships in Polygons April 24, 2013 Polygon Investigation First, we will, divide up the class into 4 groups. Pentagons, Hexagons, Heptagons, Octagons Follow the instructions on the next slide. 6 Angle Relationships in Polygons April 24, 2013 Polygon Investigation 1. Write the number of sides of your polygon on the top of your page. 2. With a protractor determine the measure of each interior angle (HINT: these are regular polygons... all interior angles are the same!!) 3. Extend each side to create the exterior angles. 4. Repeat step 2 but with the exterior angles. 5. Determine: The sum of the interior angles. The sum of the exterior angles. 7 Angle Relationships in Polygons April 24, 2013 Polygon Investigation 6. Find another person with the same polygon as you, make sure you got the same answer! 7. Find people with polygons with different numbers of sides and record their answers. 8 Angle Relationships in Polygons April 24, 2013 9 Angle Relationships in Polygons April 24, 2013 Angle Investigation 10 Angle Relationships in Polygons April 24, 2013 A New Equation! 11 Angle Relationships in Polygons April 24, 2013 Angle Relationships in Polygons Exterior Angle Theorem The sum of the exterior angles of a triangle OR a quadrilateral is 360o. any polygon 12 Angle Relationships in Polygons April 24, 2013 Angle Relationships in Polygons Interior Angle Theorem The sum of the interior angles (S) of a polygon is S = 180(n - 2) where n is the number sides. 13 Angle Relationships in Polygons April 24, 2013 Whiteboards! Interior Angle Theorem The sum of the interior angles (S) of a polygon is S = 180(n - 2) where n is the number sides. What is the sum of the interior angles of a 12sided polygon? 14 Angle Relationships in Polygons April 24, 2013 15 Angle Relationships in Polygons April 24, 2013 Whiteboards! Interior Angle Theorem The sum of the interior angles (S) of a polygon is S = 180(n - 2) where n is the number sides. If the sum of the interior angles of a polygon is 1620o, how many sides does the polygon have? 16 Angle Relationships in Polygons April 24, 2013 17 Angle Relationships in Polygons April 24, 2013 To find the sum of the angles of a polygon subtract 2 from the number of sides then multiply by 360o! To find the number of sides of a polygon divide the sum of the angles by 180o then add 2! 18 Angle Relationships in Polygons April 24, 2013 Homework Page 391 #16, 10, 11 19
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