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How do you work out an interior angle on a polygon when it has n sides?
Wiki User
∙ 12y ago
The sum of the interior angles of a polygon with n sides is 180*(n-2) degrees.
If the polygon is equiangular (ie all its angles are the same) then each of them is 180*(n-2)/n degrees.
Wiki User
∙ 12y ago
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How do you work out the exterior and interior angles of a regular polygon with W sides?
Exterior angle regular polygon = 360° ÷ number of sides = 360° ÷ W Interior angle regular polygon = 180° - exterior angle regular polygon = 180° - (360° ÷ number of sides ) = 180° - (360° ÷ W)
Work out the exterior and interior angles of a regular polygon with 8 sides?
Each exterior angle 45 degrees Each interior angle 135 degrees
How many sides does a regular polygon have if the measure of one interior angles is 144?
interior angle = (sides - 2) * 180 / sides sides * interior angle = 180 * sides - 360 sides * (interior angle - 180) = -360 sides = -360 / (interior angle - 180) sides = 360 / (180 - interior angle) So, for 144 degrees: sides = 360 / 36 = 10
Work out the number of sides of a regular polygon with an interior angle of 171 degrees?
The interior angle of a regular polygon with x sides is 180(x-2)/x. Rearranging the formula for x, the number of sides for a shape with y angles is 360/(180-y). From this formula, the number of sides is 40.
How do you work out the number of sides in a regular polygon that has an interior angle?
Restate the question: how do you find the number of sides in a regular polygon if you know the measure of an interior angle? (If this is not your question, please resubmit the question with different wording.) Subtract the interior angle from 180 deg - for example 180-160 = 20. Now divide 360 by this value: 360/20 = 18. A regular polygon with interior angles of 160 degrees has 18 sides.
Work out the number of sides of a regular polygon with the interior angle of 178?
If each interior angle is 178 degrees then the regular polygon will have 180 sides.
How do you work out the exterior and interior angles of a regular polygon with W sides?
Exterior angle regular polygon = 360° ÷ number of sides = 360° ÷ W Interior angle regular polygon = 180° - exterior angle regular polygon = 180° - (360° ÷ number of sides ) = 180° - (360° ÷ W)
How do you work out the interior and exterior angles of a regular polygon?
If the polygon has n sides (or vertices) each exterior angle is 360/n. Each interior angle = 180 - exterior angle = 180 - 360/n
Work out the exterior and interior angles of a regular polygon with 8 sides?
Each exterior angle 45 degrees Each interior angle 135 degrees
How many sides does a regular polygon have if each interior angle has a measure of 22.5?
There's no such polygon because the figures don't work out as an integer
How many sides does a regular polygon have if the measure of one interior angles is 144?
interior angle = (sides - 2) * 180 / sides sides * interior angle = 180 * sides - 360 sides * (interior angle - 180) = -360 sides = -360 / (interior angle - 180) sides = 360 / (180 - interior angle) So, for 144 degrees: sides = 360 / 36 = 10
Work out the number of sides of a regular polygon with an interior angle of 171 degrees?
The interior angle of a regular polygon with x sides is 180(x-2)/x. Rearranging the formula for x, the number of sides for a shape with y angles is 360/(180-y). From this formula, the number of sides is 40.
How do you work out the number of sides in a regular polygon that has an interior angle?
Restate the question: how do you find the number of sides in a regular polygon if you know the measure of an interior angle? (If this is not your question, please resubmit the question with different wording.) Subtract the interior angle from 180 deg - for example 180-160 = 20. Now divide 360 by this value: 360/20 = 18. A regular polygon with interior angles of 160 degrees has 18 sides.
What type of polygon does the interior angle calulation not work for Number of sides - 2 x 180?
It works for all polygons.
How do you work out the number of sides in a regular polygon that has an exterior angle?
With a regular polygon: 360/exterior angle = number of sides
How do you work out the amount of sides o a exterior angle that is 10?
To work out the number of sides, this polygon has to be a regular polygon in which all the interior angles are the same A regular polygon has exterior angles of 10o, therefore it must have interior angles of 180o - 10o = 170o Total interior angles = (Number of sides - 2)x180o Therefore each interior angle = [(Number of sides - 2)x180o]/Number of sides n = number of sides 170o = [(n-2)x180o]/n 170no = 180no-360o 360o = 10no n = 360o/10o n = 36
In a regular polygon the ratio of the measure of the exterior angle to the measure of the adjacent interior angle is 4 to 1 how many sides does the polygon have Please show your work?
This is not possible for a normal regular polygon. (A regular polygon has all equal angles and all equal sides. A normal polygon has no intersecting edges.)The smallest regular polygon is an equilateral triangle (a three sided polygon), whose exterior angle measure is twice the measure of its interior angle. A four-sided polygon (a square) has equal interior and exterior angle measures of 90⁰. Starting from a five-sided polygon, the exterior angle measure is smaller than the interior angle measure.Let's assume that the given information is true. So we need to verify it.Let's say that the interior angle of the regular polygon has a measure of x degrees, and the measure of the exterior angle of that polygon is 4x degrees.Since the sum of the interior and the exterior angles of the polygon is 180 degrees (a straight line), the interior angle is 36 degrees.4x + x = 1805x = 1805x/5 = 180/5x = 36The sum of the angles of a polygon = 180⁰(n - 2), where n is the number of the sides of the polygon.The measure of one of the angles of a polygon = 180⁰(n - 2)/n. Substituting the angle measure of 36⁰ into this formula, we have:36⁰ = 180⁰(n - 2)/n (multiply by n to both sides)36⁰n = 180⁰(n - 2)36⁰n = 180⁰n - 360⁰ (add 360⁰ and subtract 36⁰n to both sides)360⁰ = 144⁰n (divide by 144⁰ to both sides)2.5 = n !!That means that a such normal polygon does not exist.
