SOLUTION: Find the number of sides of a regular polygon with each interior angle equal to 140degree

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Question 954866: Find the number of sides of a regular polygon with each interior angle equal to 140degree

Found 2 solutions by etutorworld, Alan3354:
Answer by etutorworld(19) About Me  (Show Source):
You can put this solution on YOUR website!
Find the number of sides of a regular polygon with each interior angle equal to 140degree

The formula to find value of each interior angle can be used to find the number of sides of the regular polygon

Each Angle (of a Regular Polygon) = (n-2) × 180° / n

Here we know the value of angle i.e. 140 degree.
Substitute the same in the formula above and find the value of n

140 = (n-2) × 180° / n
Multiplying by 'n' on both sides

140n = 180n -360
140n-180n = -360

-40n = -360
Dividing by -40 on both sides we get
n = 9
the regular polygon has 9 sides i.e. its a Nonagon

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the number of sides of a regular polygon with each interior angle equal to 140degree
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Exterior angles = 180 - 140 = 40 degs
360/40 = 9 sides