find the sides of a regular polygon if each interior angle 150 degree
Answers
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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Answer:
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