Exterior Angles of a Polygon

Objectives: To verify that the sum of measures of the exterior angles of any polygon is 3600

Pre-Requisite Knowledge: Concept of triangles, quadrilaterals, pentagons and hexagons

Materials required: Glaze paper, Geometry box, A pair of scissors, sketch pens, fevistick

Preparation for the given activity: On a glaze paper make the following figures – A triangle; A quadrilateral; A pentagon; A hexagon

I

II

III

IV

Procedure: (i) Extend all the sides of the above figures to get the exterior angles of each figure

Procedure: (ii) A triangle has three exterior angles (In figure I)

Procedure: (iii) A quadrilateral has four exterior angles (In figure II)

Procedure: (iv) A pentagon has five exterior angles (In figure III)

Procedure: (v) A hexagon has six exterior angles (In figure IV)

Procedure: (vi) Now cut and separate angle 1 and angle 2 of the triangle

Procedure: (vii) Join and paste the cut out pieces of the angles, vertex to vertex with angle 3

Procedure: (viii) In the same way, cut angles a, b and c of the quadrilateral and separate them

Procedure: (ix) Join the cut out pieces vertex to vertex, of the angles to the angles to the exterior angle d of the quadrilateral

Procedure: (x) Repeat the above process with pentagon and hexagon also. Paste the cut out angles to the exterior angles of the pentagon and hexagon

Observation: We find that in each figure, when the angles are joined to the exterior angle, we get a complete angle, that is, an angle of 3600

Result: It is verified that the sum of measures of the exterior angles of any polygon is 3600