Question

the angle of
an
hexogon
are
aritbemetic
sequence prove that the
Smallest Angle is
always grater
grater than 60°​

Answer 1

Answer:

interior angle of regular hexagon is 120 degrees

Answer 2

Answer:

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°