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Question

The difference any two consecutive interior angles of a polygon is 5.If the smallest angle is 120, find the number of the sides of the polygon.

A
5
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B
45
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C
25
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D
19
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Solution

The correct options are
A 5
B 19

We know that the sum of all angles of a polygon with n sides =1800(n2)

We know that,

Sn=1800(n2)........(1)

The angles of polygon will from an A.P.

Then common difference d=50

And first term =1200

let the side of polygon=n

Then,Sn=n2[2a+(n1)d]........(2)

By equation (1) and (2) to,

n2[2a+(n1)d]=1800(n2)

n2[2×1200+(n1)50]=1800(n2)

n(2400+50n50)=3600n7200

5n2+235n360n+720=0

5n2125n+720=0

5(n225n+144)=0

n2(16+9)n+144=0

n216n9n+144=0

n(n16)9(n16)=0

(n16)(n9)=0

n=9,16

Hence, this is the answer.

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