A regular polygon has an interior angle of 172 degree Find the number of sides of this polygon
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Answer:
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Answer:
The regular polygon has 45 sides.
What are regular polygons ?
A regular polygon is one that has all of its sides be the same length and all of its interior angles be the same size. In other words, a regular polygon is a geometric shape that has equal-length straight sides and interior angles with the same degree measure. Intriguing characteristics of regular polygons include their rotational symmetry and the fact that, for a given number of sides, the ratio of their perimeter to their apothem (a segment from the polygon's center to its midpoint) is constant.
Put this formula to use to determine a regular polygon's interior angle:
(n - 2) * 180 / n
Plug in the given value of the interior angle:
172 (interior angle) = (n - 2) * 180 / n
Remove the fraction by multiplying both sides by n:
172n = 180(n - 2)
Expand the right side:
172n = 180n - 360
Subtract 172n from both sides:
8n = 360
Divide both sides by 8:
n = 45
Therefore, the regular polygon has 45 sides.
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