Find the measure of an exterior angle of a regular polygon if its each interior angle is 140◦
Answers
Method 1: 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.
exterior angle sum property= 360°
exterior angle= 360/n
=360/9
=40°
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.
exterior angle sum property= 360°
exterior angle= 360/n
=360/9
=40°
so measure of exterior angle is 40°
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