Question

The angles of a hexagon are in arithmetic sequence. prove that its smallest angle is greater than 60°​

Answer 1

Given :  smallest angle is greater than 60 degree

To find : prove that its smallest angle is greater than 60 degree

Solution:

Sum of angle of polygon of n sided = (n- 2) * 180°

Hexagon has 6 sides  so

Sum of all angles = (6 - 2) * 180° = 720°

Let say smallest angle =  a°      a  > 0

and d° is the common difference  

then largest angle = a + 5d

largest angle should be less than 180°

=> a + 5d <  180°

=> a + 5d = 180 - k   k > 0

Sum of all angles

a + a + d  + a + 2d + a + 3d + a + 4d + a + 5d  = 720

=> 6a + 15d  = 720

=> 2a + 5d  = 240

=> a  + a + 5d  =  240

=> a  + 180 - k  =  240

=> a = 60 + k

=> a > 60

QED

Hence proved

smallest angle is greater than 60°

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