Calculate the number of sides of a regular polygon whose interior angles are each 150
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6
Solution :-
The measure in degrees of an interior angle of a regular polygon is given by 180*(n - 2)/n.
Given that the measure of each interior angle of a regular polygon is 150°.
So, we can say that -
180*(n - 2)/n = 150
⇒ (180n - 360)/n = 150
⇒ 180n - 360 = 150n
⇒ 180n - 150n = 360
⇒ 30n = 360
⇒ n = 360/30
⇒ n = 12
So, the given regular polygon has 12 sides.
The measure in degrees of an interior angle of a regular polygon is given by 180*(n - 2)/n.
Given that the measure of each interior angle of a regular polygon is 150°.
So, we can say that -
180*(n - 2)/n = 150
⇒ (180n - 360)/n = 150
⇒ 180n - 360 = 150n
⇒ 180n - 150n = 360
⇒ 30n = 360
⇒ n = 360/30
⇒ n = 12
So, the given regular polygon has 12 sides.
Answered by
3
Answer
A = 180(n-2)/n
150 = 180(n-2)/n
150n = 180n - 360
360 = 30n
n = 12
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