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Transcript
3.3 Angles of Polygons Essential Question: How can you find the sum of the interior/ exterior angle measures of a polygon? Polygon: A closed figure with straight sides and does not have any lines that cross through the middle. Vocabulary Polygon: A closed figure with straight sides and does not have any lines that cross through the middle. Thumbs: Polygons or Not Polygons? Polygon Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon n-gon Sides 3 4 5 6 7 8 A diagonal: a line segment connects two non-adjacent vertices of a polygon Diagonal How to find the sum of the interior angles: 1st:Draw a line from one vertex to another vertex. Repeat until you have connected all vertices (lines can’t overlap) 2nd: The quadrilateral has 4 sides and is made up of 2 triangles 3rd: A triangle has 180 4th: Therefore the sum of the interior angles is (2 triangles x 180) for a sum of 360 Diagonal 180 180 Divide each polygon into triangles Sum of interior angles = (4 triangles)180 Therefore the sum of the interior angles is 720 180 OR 180 180 180 180 180 180 180 Draw it How to find the sum of the interior angles: The pentagon has 5 angles and is made up of 3 triangles Therefore the sum of the interior angles is 180(3) = 540 180 180 180 OR 180 180 180 Find the missing interior angle measures of a pentagon Find the missing interior angle measures of a pentagon Find the missing angle Draw it Regular Polygon: A polygon where all sides are congruent and all interior angles are congruent. x x x x x x Step 1: 180 180 180 180 There are 6 sides and 4 triangles: Sum = (n - 2)180 Therefore the sum of the interior angles is 720 Step 2: Divide sum of interior angles by # of angles (6 angles) 720 ÷ 6 = 120 Or: x x x + x + x + x + x + x = 720 6x = 720 x x x x x = 720 Vocabulary Convex Polygon: A polygon where every line segment connecting any two vertices lies entirely inside the polygon. Concave Polygon: A polygon where at least one line segment connecting any two vertices lies entirely outside the polygon. Draw it
