x = 360 / (180 - y) y = 108 Therefore, if y is 108, x = 5 Each angle deviates an equal amount from 180 degrees. The total deviation must add up to 360. Hence, the above equation. The value of y must be such that x will be a whole number, no fractions. If the result of the equation is not a whole number, you don't have a regular polygon; the angles are not all the same.
Another way to look at this:
Every polygon has interior angles adding up to 180(n-2). In this polygon, the interior angles add up to 108n, where n is the number of sides. 180(n-2)=108n 180n -360 -108n =0 72n = 360 n= 5 ^^ the polygon could also have 18 sides.
Since the interior angle measure of the regular polygon is 140⁰, its exterior angle measure is 180⁰ - 140⁰ = 40⁰. Since the sum of the exterior angle measures is 360⁰, the polygon has 360⁰/40⁰ = 9 sides.
The method of finding the sum of the interior angles of a polygon is by multiplying the (number of sides)-2 by 180, so the sum of the interior angle measures in a 25-sided polygon would be 23*180, or 4140 degrees.
A regular polygon has sides of equal length, as well as interior angles of equal measure. But for any regular polygon, the sum of the measures of the exterior angles is 360 degrees. You can use this information to find out the measure of an interior angle, because the sum of the measures of each interior/exterior pair of angles is always 180 degrees. So to find the answer to this problem, divide 360 by 7. Each exterior angle is about 51.4 degrees. Subtract that number from 180. Each interior angle is about 128.6 degrees.
180 sides!
We have the interior angle 144∘ . We can find the number of sides using the formula as follows. Thus, the polygon has 10 angles and 10 sides.
A four-sided regular polygon (square or rectangle) has 900 interior angles.
The interior angle of any regular polygon can be calculated using the formula 180 * (n - 2) / n, where n is the number of sides. In this case, since each exterior angle measures 72 degrees, the interior angle would be 180 - 72 = 108 degrees. So the measures of the interior angles in this regular polygon would be 108 degrees.
5 sides and it is a regular pentagon
As the number of sides in a regular polygon increases, the angle increases. This occurs as a function where each interior angle measures (180*(n-2)) / n, where n is the number of sides.
A polygon with interior angle measures of 108 would be a pentagon
For the interior angle of a regular polygon to be greater than 130° then the exterior angle must be less than 50°. The exterior angles of a regular polygon total 360°. 360/50 = 7.2 ....this needs to be rounded up to the next whole number. Therefore a regular polygon with 8 or more sides has interior angles measuring 130° or greater.
Since the interior angle measure of the regular polygon is 140⁰, its exterior angle measure is 180⁰ - 140⁰ = 40⁰. Since the sum of the exterior angle measures is 360⁰, the polygon has 360⁰/40⁰ = 9 sides.
The sum of the interior angles of a polygon is 2n - 4 right angles where n is the number of sides. When n = 21 then 2n - 4 = 42 - 4 = 38 right angles = 38 x 90 = 3420°. NOTE : If the polygon is a regular polygon then each interior angle measures 3420 ÷ 21 = 162.86°.
If its a regular polygon then 180-interior angle and divide the answer into 360 which will give the number of sides of the polygon.
170n = 180n - 360 so 10n = 360 so n = 36
The equation for finding the interior angle measures of a regular n-gon is (n-2)*180/n. Thus, if this is set equal to 176 and solved for n, n is found to be 90. Therefore, a regular polygon with each interior angle measure equal to 176, has 90 sides.
If each interior angle is 178 degrees then the regular polygon will have 180 sides.