9. Each interior angle of a regular polygon is
140°. Find the number of its sides.
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Answer:
Since the interior angle 140 degrees, the supplement of this is the exterior angle and equal to 40 degrees. Hence the number of sides is 360/40 = 9 sides.
Method 2: Since the exterior angle 140 degrees, The sum of the interior angles = (2n - 4)* right angles. So 140n =(2n - 4)* right angles, or
140n =(2n - 4)*90, or
140n = 180n - 360, or
40n = 360, or
n = 9 sides.
Hence the number of sides is 9 sides.
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