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3.4 Sum of exterior angles of a Polygon

Figure 3.4

Figure 3.4 shows a pentagon. Its external angles are named from a to e. The aim is to find the sum of these five angles.

It is known that the sum of internal angles of a Pentagon

= (5 - 2 ) ´ 1800

= 3 ´ 1800

= 540

\ each interior angle of the pentagon measures

5400 / 5 = 1080

The interior and exterior angles form linear pairs and hence are supplementary.

\ Each exterior angle measures 1800 - 1080 = 720

\ Sum of five exterior angles = 5 ´ 72 = 3600

It can be proved that the sum of the exterior angles for any polygon is 360 0.

Sum of interior angles of an n sided polygon = ( n - 2 ) 1800.

\ Measure of each internal angle =

\ Each exterior angle =

\ Sum of n exterior angles =

=

=

Conclusion : The sum of interior angles of a polygon is dependent on the number of sides but the sum of the exterior angles is always 3600.

Index

3. 1 Definition
3. 2 Terminology
3. 3 Sum Of Interior Angles Of A Polygon
3. 4 Sum Of Exterior Angles Of A Polygon
3. 5 Trapezoids
3. 6 Parallelogram
3. 7 Square, Rectangle And Rhombus

Chapter 4

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