How many sides does a regular polygon have if its interior angle have 165 degrees
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The sum of the interior angles in any polygon is 180(n - 2) degrees. Then, since each angle in a regular polygon is the same, each interior angle has a measure of 180(n - 2)/n degrees.
Given that the interior angle is 165 degrees, we have:
180(n - 2)/n = 165
==> 180n - 360 = 165n
==> 15n = 360
==> n = 24.
Thus, the polygon has 24 sides.
I hope this helps!
Given that the interior angle is 165 degrees, we have:
180(n - 2)/n = 165
==> 180n - 360 = 165n
==> 15n = 360
==> n = 24.
Thus, the polygon has 24 sides.
I hope this helps!
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