Question

Find the number of sides of a regular polygon whose interior angle is 156 degrees

Answer 1

Find the number of sides of the regular polygon whose interior angles each measure 156 degrees
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Ext angle = 180 - Int angle = 24
n = 360/24 = 15 sides

Total interior angles = (n-2)*180
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So, the average interior angle = ( (n-2)*180 ) / n
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((n-2)*180)/n = 156
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(n-2)*180 = 156n
180n -360 = 156n
24n = 360
n = 15
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The polygon has 15 sides.

Answer 2

Recall that the sum of the exterior angles is 360, and that an interior angle + an exterior angle = 180

Thus, if the interior angles are each 156, the exterior angles are each 180-156=24.

Now take 360/24 (because each exterior angle is 24 and they need to add to 360), you get 15. Thus, there are 15 sides.