Question

the exterior angle of a pentagon are in the ratio of 1 ratio 2 ratio 3 ratio 4 ratio 5 ratio. find all the interior angle of the Pentagon .

Answer 1

Let the first external angle be x. Then sum of all external angles is

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

15x=360

x=24

So first internal angle is 180-x (Because each pair of internal angle and corresponding external angle form a linear pair. i.e. sum of internal angle and corresponding external angle is 180)

First angle is 180-x = 180-24 = 156

Second angle is 180-2x = 180-48 = 132

Third angle is 180-3x = 180-72 = 108

Fourth angle is 180-4x = 180-96 = 84

Fifth angle is 180-5x = 180-120 = 60