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The angles that cannot be an interior angle in a regular polygon are 40 72° 108° 148°
A polygon is a closed polygonal chain made up of a limited number of straight line segments and is a type of planar figure in geometry. A polygon is an area that is bordered by a bounding circuit, a bounding plane, or both. A polygonal circuit's segments are referred to as its edges or sides.
A regular polygon has equal internal angles all around. A polygon's interior angle is calculated using the following formula: interior angle of a polygon = sum of interior angles number of sides. The total of a polygon's outer angles is 360°.
Given the different angles in degree.
We have to find angle which can't be interior angle in a regular polygon
We apply the formula for each angle = (n - 2) 180 / n to determine the size of each interior angle of a regular polygon.
Let the interior angle be 108 degree
(n - 2) 180 / n = 108
n = 0.5 not possible
Let the interior angle be 148 degree and 179 degree
(n - 2) 180 / n = 148
n = 1.125 not possible
(n - 2) 180 / n = 179
n = 36 possible
Let the interior angle be 40 degree and 72 degree
(n - 2) 180 / n = 40
n = 0.9 not possible
(n - 2) 180 / n = 72
n = 0.33 not possible
Hence angles that cannot be an interior angle in a regular polygon are 40 72° 108° 148°
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The angles that cannot be an interior angle
in a regular polygon are 40 72° 108° 148°
A polygon is a planar figure in which closed polygonal chain made up of a limited number of straight line. A polygon is an area that is bounded by a bounding circuit or a bounding plane or both.
A regular polygon is a polygon which has equal internal angles all around it.
In a polygon, the interior angle = sum of interior angles number of sides.
Total outer angle of a polygon is 360°.
Here we have to find the angle which can't be an interior angle of a regular polygon.
The size of each interior angle of a regular polygon = [(n-2)×180°] /n
1. 108 degree
[(n-2)×180°] /n = 108
180n - 360 = 108n
72n=360
n = 0.2 This is not possible since n is a natural number
2. 148 degree
[(n-2)×180°] /n = 148
180n - 360 = 148n
72n=360
n = 0.2 This is not possible since n is a natural number
Let the interior angle be 148 degree and 179 degree
(n-2) 180 / n = 148
n = 1.125 not possible
(n-2) 180 / n = 179
n = 36 possible
Let the interior angle be 40 degree and 72 degree
(n-2) 180 / n = 40
n = 0.9 not possible (n-2) 180 / n = 72
n = 0.33 not possible
Hence angles that cannot be an interior angle in a regular polygon are 40 72° 108° 148°
