Question

The angles of a hexagon are in arithmetic sequence.its largest angle is 140°.can the smallest angle be 60°?why?

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°

Please mark me as the brainliest

Answer 2

Answer:- 60°

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Step-by-step explanation:

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°

Hope it helps ❣️