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How many sides has a regular polygon whose interior angle is 11 times its exterior angles?
The measure of an interior angle in degrees of a regular polygon of n sides is given by the formula: 180 x (n-2) / nThe measure of an exterior angle in degrees of a regular polygon of n sides is given by the formula: 360/nIf the interior angle is 11 times the exterior angle, then:180 (n-2)/n = 11 x 360/nthen: 180 n - 360 = 11 x 360, or180 n = 12 x 360that its solution gives n = 24Accordingly, the answer is that the number of sides of this polygon is 24
Find the number of sides of a regular convex polygon whose angle is 40degrees?
140
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.
How many sides does a regular polygon have if the measures of each exterior angle equals 12 degrees?
The regular polygon whose exterior angle measure is 12 degrees, has 30 sides (360/12, since the exterior angles on any polygon always add up to 360 degrees).
How many sides in regular n-gon whose sum of interior angles is 1080?
sum of interior angles = (n-2)180=1080 1080/180=n-2 6=n-2 8=n
What is the name of the regular polygon whose interior angle is treble ist exterior angle?
It is a regular octagon which has 8 sides
Which regular polygon has an interior angle whose measure is 108 degree?
hextogonImproved Answer:-A regular pentagon which has 5 sides
How many sides has a regular polygon whose interior angle is 11 times its exterior angles?
The measure of an interior angle in degrees of a regular polygon of n sides is given by the formula: 180 x (n-2) / nThe measure of an exterior angle in degrees of a regular polygon of n sides is given by the formula: 360/nIf the interior angle is 11 times the exterior angle, then:180 (n-2)/n = 11 x 360/nthen: 180 n - 360 = 11 x 360, or180 n = 12 x 360that its solution gives n = 24Accordingly, the answer is that the number of sides of this polygon is 24
How many sides a regular n gon whose sum of interior angle is 1080?
The sum of the interior angles of an n-gon (regular or irregular) = (n-2)*180 = 1080 Therefore (n - 2) = 8 and so n = 10.
What is the name of th regular polygon whose interior angle is treble its exterior?
It is a regular 8 sided octagon whose interior angles are 135 degrees and its exterior angles are 45 degrees
How do you find the number of sides of a polygon whose interior angle sum is 5580?
(5580 + 360)/180 = 33 sides
What is the definition of central angle of a regular polygon?
an angle whose vertex is the center of the polygon and whose sides pass through adjacent vertices.
What is the name of the regular polygon whose interior angle is treble its exterior angle?
Interior angle = 3 x exterior angle. Hence Int Ang + Ext Ang = 180 Substituting 3 x Ext + Ext = 180 4 Ext = 180 Ext Angle = 180 / 4 = 45 degrees. And Exterior Ang;e = 360 / number of sides. number of sides = 360/ exterior angle No. of sides = 360/45 = 8 Hence the number of sides of the polygon is '8' . It is named as an OCTAGON.
Find the number of sides of a regular convex polygon whose angle is 40degrees?
140
Calculate the number of sides of a regular polygon whose interior angles are each 165 degrees?
14 sides in the polygon
Which of these two regular polygons has the largest interior angle triangle or heptagon?
It is the regular 7 sided heptagon whose interior angles are greater than the regular 3 sided triangle
How many sides in a polygon whose interior angle is 174?
It could be three. It could be a triangle with angles of 174, 3 and 3 degrees. If it is a REGULAR polygon, though, there is a more specific answer. Interior angle = 174 deg implies exterior angle = 6 deg. Sum of ext angles = 360 deg so there must be 360/6 = 60 sides to the polygon.
