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How many sides does a polygon have if the sum of its interior angles is equal to the sum of its exterior angles?
Wiki User
∙ 14y ago
The sum of the exterior angles of all polygons equals to 360⁰.
Since only the sum of the interior angles of all quadrilaterals equals to 360⁰, the polygon must have 4 sides.
Wiki User
∙ 14y ago
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How many sides does a polygon have if the interior angles equal 180 degrees?
If all of the interior angles of the polygon add up to 180 degrees, then the polygon is a triangle.
What does all the measures of a regular polygon have to equal up to?
The exterior angles of any polygon add up to 360.
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.
What is the sum of a polygon with interior angles and 39 sides?
The sum of the interior angles of any regular polygon of n sides is equal to 180(n - 2) degrees. 6660 degrees.
Exterior angle property of a triangle?
measure of exterior angle of triangle is equal to sum of interior angles. for eg. In triangle ABC, angle C is exterior angle angle A and angle B are interior angles so, C=A+B
What type of regular polygon has equal interior and exterior angles?
A quadrilateral.
A regular polygon with interior and exterior angles that equal?
Square or rectangle
Is the sum of the remote interior angles in a polygon equal to the exterior angle?
No.
Are Exterior and interior angles equal to 360?
No because an exterior angle and an interior angle of a polygon add up to 180 degrees but exterior angles around a polygon add up to 360 degrees
How many sides does a regular polygon have if its exterior angles are equal to its interior angles?
4 such as a square
What polygon has the sum of the interior angles equal to two times the sum of the exterior angles?
hexagon
How many sides does a polygon have when the sum of its interior angles is equal to the sum of its exterior angles?
Four sides
What properties of a polygon make it regular?
When all sides are equal and all interior and exterior angles are equal.
What are the properties of regular polygon?
Interior angles are equal and sides are equal in length and exterior angles add up to 360 degrees
Interior and exterior angles of a 30 sided polygon?
The total of the interior angles equal 5040, and each angle measures 168 degrees The total of the exterior angles equal 360, and each angle measures 12 degrees
What polygon does the sum of the measures of interior angles equal the sum of the measures of the exterior angles?
A 4 sided quadrilateral has interior angles that add up to 360 degrees and its exterior angles add up to 360 degrees
What is the interior and exterior angle of a p sided polygon?
Sum of interior angles = (p-2)*180 degrees Sum of exterior angles = 360 degrees You can go further than that only if the polygon is regular. In that case, all the interior angles are equal and each one is (p-2)*180/p degrees; and all the exterior angles are equal and each is 360/p degrees.
