Question

The interior angle of a polygon are in A.P.
The smallest angle is 94º and the common
difference is 7º. Find the number of sides of
the polygon.​

Answer 1

Answer:

Number of sides=5

Step-by-step explanation:

Let no of sides=x

then sum of angles=(2x-4)90

Now in AP

a=94 d=7,n=x

then sum of the AP

=x/2(2*94 + (x-1)*7)=(2x-4)90

x(188+7x-7)=180(2x-4)

x(7x+181)=360x-720

7x²+181x-360x+720=0

7x²+181x-360x+720=0

7x²-179x+720=0

x=( 179 ±√(32041-4*7*720)/14

=( 179 ±√32041-20160/14

=(179±√11881)/14

=(179±109)/14

x=179-109/14

or x=70/14=5

Hence x=5

Number of sides=5

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for other value of x=179+109/14=288/14=20.57

this is not perfect no. so can not be no. of sides

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