3.3. Sum of the Measures of the Exterior Angles of a Polygon
Draw a polygon on the floor, using a piece of chalk. (In the figure, a pentagon ABCDE is shown). We want to know the total measure of angles, i.e., m ∠1 + m∠2 + m∠3 + m∠4 + m∠5. Start at A. Walk along AB . On reaching B, you need to turn through an angle of m∠1, to walk along BC. When you reach at C, you ned to turn through an angle of m∠2 to walk along CD. You continue to move in this manner, until you return to side AB. You would have in fact made one complete turn. Therefore, m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360°. This is true whatever be the number of sides of the polygon. Therefore, the sum of the measure of the external angles of any polygon is 360°.
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