Question

the angles of a Pentagon are in arithametic sequence prove that it's smallest angle is greater than the 36?​

Answer 1

Answer:

37

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Answer 2

Answer:

Yes , smallest angle is 36

Step-by-step explanation:

The sum of all the angles in a pentagon are 540

Number of angles in a pentagon be 5

Given the angles are in arithmetic progression , the first angle be a, and the common difference be d

Sum of an arithmetic progression  of n terms is given by Sum = (2a+(n-1)d)×n÷2

In this case n=5 and the total sum is 540

For ease of simplification I am considering the 5 angles to be  a-2d, a-d, a, a+d, a+2d

By data the sum of all  the angles of = 540

which gives as 5a=540

  a= 108

The smallest angle is a- 2d  and I am considering it to be 36

which gives d=36

And now evaluating all the angles with the smallest angle as 36 and finding their sum is equal  to exact 540 and anything lesser than that will result in sum less then 540, hence the smallest angle should be greater than or equal to 36