SOLUTION: A polygon has n sides.one of its interior angles is 126 while the other angles are each equal to 162,find the value of n.

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Question 1026777: A polygon has n sides.one of its interior angles is 126 while the other angles are each equal to 162,find the value of n.
Answer by ikleyn(52817) About Me  (Show Source):
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A polygon has n sides. One of its interior angles is 126 while the other angles are each equal to 162. Find the value of n.
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126 + (n-1)*162 = (n-2)*180.


Left side is the sum of interior angles of the given n-gon.

Right side is the sum of interior angles of the general n-gon.

Solve for n and obtain the answer.

126 - 162 + 2*180 = 180n -162n,

324 = 18n,

n = 324%2F18 = 18.