Interior/Exterior Angles in Regular Polygons R.4.G.2 Solve problems using properties of polygons: sum of the measures of the interior angles of a polygon.

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Presentation transcript:

Interior/Exterior Angles in Regular Polygons R.4.G.2 Solve problems using properties of polygons: sum of the measures of the interior angles of a polygon interior and exterior angle measure of a regular polygon or irregular polygon number of sides or angles of a polygon

Regular Polygon: a polygon with all congruent sides and all congruent angles Diagonal: a line drawn through the interior of a polygon from a vertex to a non-consecutive vertex.

TriangleQuadrilateralPentagon HexagonHeptagonOctagon

PolygonNumber of Sides Number of triangles formed by drawing all diagonals from one vertex Sum of angle measures in each triangle The sum of the interior angles Triangle Quadrilateral Pentagon Hexagon Heptagon

PolygonNumber of Sides Number of triangles formed by drawing all diagonals from one vertex Sum of angle measures in each triangle The sum of the interior angles Octagon Nonagon Decagon N-gon 20-gon

The sum of the measures of the interior angles of an n-gon is 180(n-2)

Find the sum of the interior angles of the following polygons: Dodecagon 18-gon

Draw an exterior angle at each vertex of the polygons. Measure each exterior angle and find the sum of all the exterior angles for each polygon. Record your results in the table.

PolygonNumber of SidesMeasures of one Exterior Angle Sum of the Measures of the Exterior Angles Triangle Quadrilateral Pentagon Hexagon n-gon 20-gon

The sum of the exterior angles of any polygon is 360 degrees!

To find one exterior angle of any polygon with “n” sides: Interior Angle + Exterior Angle = 180 o

Find the measure of each interior and exterior angle of a regular octagon. n = Exterior angle = Interior angle = o 45 o

Find the measure of each interior and exterior angle of a 22-gon. Interior: o Exterior: 16.4 o

If the exterior angle measures 40 o in a regular polygon, how many sides does it have?

If the exterior angle measures 120 o in a regular polygon, how many sides does it have?

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