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A regular polygon with interior angles of 144 degrees has 10 sides. Using the fact that a regular n-gon has interior angles of degree (n-2)*180/n, you can solve for the number of sides fairly easily.
It will have (1440+360)/180 = 10 sides which is a decagon
triangle
(n-2)*180 = sum of interior angles when n is the number of sides of the polygon
A relevant general formula is that the sum of the interior angles of a regular polygon equals 180(n-2), where n is the number of sides. Also, all of the interior angles of a regular polygon are equal. Therefore, 180(n - 2) = 144n in the instance given, or: 180n - 360 = 144n, or (180 - 144)n = 360, or 36n = 360, or n = 10.
There is no such regular polygon with 45 degree interior angles; the smallest interior angles in regular polygons are 60 degrees, which is found in a triangle.
No. To elaborate, the smallest regular polygon, an equilateral triangle, has 60 degree interior angles. The next larger one, a square, has 90 degree interior angles. In fact, for any regular polygon, the interior angles measure 180*(n-2)/n degrees, where n is the number of sides. No polygon has less than 3 sides. Thus, no regular polygon can have interior angles less than 60 degrees.
A regular 12 sided polygon each interior angle measures 150 degrees
360degrees/335 interior angles=1.075degrees
If its a regular polygon and each interior angle measures 175.2 degrees then it will have 75 sides
No. If the interior angles are 158o, then the exterior angles are 180o - 158o = 22o For all polygons, the sum of the exterior angles is 360o. For a regular polygon, they are all the same, so: exterior_angle x number_of sides = 360o ⇒ number_of_sides = 360o ÷ exterior_angle = 360o ÷ 22o = 164/11 A polygon must have a whole number of sides, thus there is no regular polygon with all interior angles 158o
A regular polygon with interior angles of 144 degrees has 10 sides. Using the fact that a regular n-gon has interior angles of degree (n-2)*180/n, you can solve for the number of sides fairly easily.
It will have (1440+360)/180 = 10 sides which is a decagon
By definition a regular polygon cannot be concave. Concave polygons contain one or more interior angles that are greater than 180 degrees, and regular polygons can never have an interior degree greater than 180 degrees.
triangle
(n-2)*180 = sum of interior angles when n is the number of sides of the polygon
Sum of interior angles = (n-2)*180 degrees = 1080 deg So (n-2) = 1080/180 = 6 => n = 8. The polygon is, therefore, an octagon. However, there is no reason to assume that the interior angles of this polygon are all the same - they could all be different with the only constraint being their sum. IF, and that is a big if, the polygon were regular, then all its angles would be equal and each interior angle = 1080/8 = 135 degrees.