360/n
By dividing the given exterior angle into 360 degrees tells you how many sides the polygon has.
180-interior angle = exterior angle 360/exterior angle = number of sides
The sum of the exterior angles of any polygon is 360o. For a regular polygon, they are all the same, so 360o divided by the size of exterior angleo will give you how many sides the polygon has.The interior and exterior angles of a polygon are supplementary and so sum to 180o.So given the internal angle, subtract from 180o and then divide into 360o and you will have the number of sides.Interior angle = 144oexterior angle = 180o - 144o = 36o. number of sides = 360o / 36o = 10 (a decagon).Interior angle = 140oLeft as an exercise for the reader. reader:ext.a.=180-140=40n. of s.=360/40=9Thanks a lot!
It is given by the formula (number of sides - 2) * 180 degrees.
360/exterior angle = number of sides
180-interior angle = exterior angle 360/exterior angle = number of sides
48 sides A formula for finding the number of sides of a regular polygon given an interior angle: 360/(180-angle)=sides
1. Use a protractor. 2. If given the interior angle, use the linear pair postulate. (180-interior angle measure) 3. If given that the polygon is regular, divide 360 by the number of angles.
In a polygon with n sides, the sum of the interior angles is given by (n-2) * 180 degrees. Each triangle has interior angle sum of 180 degrees. Therefore, the number of triangles that can be formed in a polygon is equal to (n-2) * 180 / 180, which simplifies to (n-2). In other words, the number of triangles is two less than the number of sides in the polygon.
To find the number of sides in a regular polygon with a given interior angle, you can use the formula: ( n = \frac{360}{180 - \text{angle}} ). For a polygon with a 72-degree interior angle, this would be ( n = \frac{360}{180 - 72} = \frac{360}{108} ), which simplifies to ( n = \frac{360}{108} = \frac{10}{3} ), approximately 3.33. Since the number of sides must be a whole number, a polygon cannot have an interior angle of 72 degrees, indicating that the angle pertains to a different context in polygon geometry.
To find the number of sides of a polygon given an interior angle, you can use the formula for the interior angle of a regular polygon: ( \text{Interior Angle} = \frac{(n-2) \times 180}{n} ), where ( n ) is the number of sides. Setting this equal to 3240 and solving for ( n ), we get: [ 3240 = \frac{(n-2) \times 180}{n} ] Multiplying both sides by ( n ) and rearranging gives ( n = 20 ). Therefore, the polygon has 20 sides.
In a regular 10-sided polygon, each interior angle measures 144 degrees. This can be calculated using the formula: (n-2) x 180 / n, where n is the number of sides. The exterior angle of a regular polygon is always supplementary to the interior angle and can be calculated by subtracting the interior angle from 180 degrees. Therefore, the exterior angle of a regular 10-sided polygon would be 36 degrees.