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The Interior Angles of Polygons Jessica King-Instructional Presentation Objective To model the interior angles of polygons To apply the formula of the sum of interior angles accurately What Is A Polygon? A polygon is a two-dimensional shape made of straight line segments, and the shape is closed. A closed shape means that all sides are connected Interior Angles of Polygons Definition: An interior angle is an angle inside the shape Sum of A Triangle’s Interior Angles The Interior Angles of a Triangle add up to 180° Sum of A Quadrilateral’s Interior Angles A quadrilateral can be drawn as two triangles… So the Sum of the Interior Angles of a Square is 180+180 = 360° Sum of the Interior Angles of a Polygon with n number of sides We can draw line segments from one angle to another to create multiple triangles out of each polygon… Activity: Constructing Triangles in a Polygon The Sum of Interior Angles Formula The sum of interior angles =180°(n-2) Where n is the number of sides of the polygon Example What is the Sum of the Interior Angles of an Octagon? An octagon has 8 sides 8=n Sum of Interior Angles = 180(n-2) =180(8-2) =180(6) =1080° The Sum of the Interior Angles of an Octagon is 1080°