Question

Answer this question

Answer 1

Answer:

30 or 3

Step-by-step explanation:

according to ques.:

a=52 , d=8

we need to find n

sum of interior angles =(n-2)180     -----1

also, sn=n/2[2a+(n-1)d]       ____2

therefore,

eq. 1 and 2 are equal   (sum of n terms and sum of interior angles)

n/2[2a+(n-1)d] = (n-2)180

putting the respective values

n/2[2(52)=(n-1)8] = (n-2)180

n/2(104+8n-8) = 180n-360

n/2(96+8n) = 180n-360

n/2*2(48+4n) = 180n-360   [2 commom from(96+8n)]

n(48+4n) = 180n-360

4n²+48n = 180n-360

4n²+48n-180n+360 = 0

4n²-132n+360 = 0

(dividing whole equation by 4)

n²-33n+90 = 0

(solving with splitting the mid term)

 = (n²-30n)(-3n+90)

 = n(n-30)-3(n-30)

 = (n-3)(n-30)

 n=3,30

therefore no. of sides can be 3 or 30.

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