Math, asked by KartavyaDama, 6 months ago

find the sides of a regular polygon if each interior angle 150 degree​

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Answered by Anonymous
5

Answer:

Hence, number of diagonals we get

= (n-3) +(n-3) +(n-3) + …… ntimes.

But, exactly half of the above given number of diagonals are repeating….

Like, in a pentagon, if vertices are 1,2,3,4,5

Then joining vertices by following way..

(1, 3)(1,4), (2,4)(2,5), (3,1)(3,5), (4,1)(4,2), (5,2)(5,3)

we get (5–3) + (5–3) + ……. 5 times

= 2*5= 10 segments in which exactly half will be repeated ones.

So, no of diagonals = 10÷2 = 5

So, Formula: no of diagonals = {(n-3)*n}÷ 2

Now, in the above question, measure of each angle of a regular polygon = 150°

=> (n-2)*180° /n = 150°

=> 180n - 150n = 360

=> 30n = 360

=> n = 12

=> given regular polygon is a 12 sided regular polygon.

So, number of diagonals = {(12–3)*12}÷2

= (9 *12)/2 = 108/2

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Answered by Anonymous
0

Answer:

hyy here is your answer ♦️♦️

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