Question

The interior angles of a polygon are in A.P. If the smallest angle is 100° and the common difference
is 4°, then the number of sides is
JA ]
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Answer 1

Answer:

sumofinterioranglesofannsidedpolygon=180(n−2)

Angles are in AP

Smallest angle =a=100

0

Common difference =d=4

0

Sum of n terms

2

n

[2a+(n−1)d]

Sum of n terms

2

n

[200+(n−1)4]

sumofterms⇒n[100+2(n−1)]

......(2)

(1)=(2)

⇒n[100+2(n−1)]=180(n−2)

⇒100n+2n

2

−2n=180n−360

⇒2n

2

=82n−360

⇒n

2

−41n+180=0

⇒n

2

−36n−5n+180=0

⇒n(n−36)−6(n−36)=0

⇒(n−5)(n−36)=0

⇒n=5 or 36

Step-by-step explanation:

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