Question

The exterior angles of a polygon are in the ratio 1:2:3:4, find all the exterior angles.​

Answer 1

Given ratio is 1: 2 : 3: 4: 5.

Let the exterior angles of a pentagon are in the ratio 1x,2x,3x,4x,5x.

We know that sum of exterior angles of a pentagon = 360.

1x + 2x + 3x + 4x + 5x = 360

15x = 360

x = 360/15

x = 24.

The exterior angles of the Pentagon are  24, 2(24),3(24),4(24),5(24)  

                                                                   = 24,48,72,96,120.

We know that sum of interior angles of a Pentagon = 180.

180 - 24, 180 - 48,180 - 72,180 - 96,180 - 120.

= 156,132,108,84,60.

Therefore the interior angles of a Pentagon are 156,132,108,84,60.

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