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What is the set of polygons for which the number of diagonals is greater than the sum of the measures of the angles?
Wiki User
∙ 14y ago
n-sided polygons with n greater than or equal to 362.
The number of diagonals of an n-sided polygon is n(n-3)/2. The sum of the measures of the angles in an n-sided polygon is 180(n-2).
So for the condition in the problem to be true,
n*(n-3)/2>180(n-2)
64979>64800
Simplifying and bringing all of the terms to the left-hand side:
n2-363n+720>0
Find the roots of n2-363n+720=0, using the quadratic formula:
n=(363+/-sqrt(3632-4(1)(720)))/2, or approximately (363+/-359.01)/2, so the roots are approximately 2 AND just more than 361
Consider each of the intervals: (-inf, 2); (2, 362); (362, inf) [since we are only interested in whole numbers, we can use the smallest whole number greater than the root]:
Plugging in one point from each interval, we see the given inequality is true in the first interval, false in the second interval, and true in the third interval. Since we are only interested in n>2 (since this is a polygon), we get the set of all polygons, with n>=362 sides. For n=362, we have 64979 diagonals and 64800 degrees for the sum of the interior angles.
Wiki User
∙ 14y ago
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what is the name of polygons you given to a shape?
There are lots of different types of polygons Polygons are classified into various types based on the number of sides and measures of the angles.: Regular Polygons Irregular Polygons Concave Polygons Convex Polygons Trigons Quadrilateral Polygons Pentagon Polygons Hexagon Polygons Equilateral Polygons Equiangular Polygons
How many ways can you find the sum of measures of the exterior angles of a polygon?
The sum of a regular polygons exterior angles always = 360
How do you find the measures of a rhombus with two diagonals?
That will depend on the lengths of the diagonals of the rhombus which are of different lengths and intersect each other at right angles but knowing the lengths of the diagonals of the rhombus it is then possible to work out its perimeter and area.
What shape have diagonals that bisect each other at right angles?
Square, rhombus, regular octagon, other regular polygons with 4n sides (where n is an integer).
Do all polygons have congruent angles?
No only regular polygons have congruent angles.
Who diagonals bisect opposite angles?
The principal diagonals of all regular polygons.
What polygons has two diagonals that are perpibdicular?
A square, a rhombus and a kite all have perpendicular diagonals that intersect at right angles
Which polygons have interior angles in which the sum of the measures of the angles is 720 degrees?
octagon
what is the name of polygons you given to a shape?
There are lots of different types of polygons Polygons are classified into various types based on the number of sides and measures of the angles.: Regular Polygons Irregular Polygons Concave Polygons Convex Polygons Trigons Quadrilateral Polygons Pentagon Polygons Hexagon Polygons Equilateral Polygons Equiangular Polygons
What are angles segments triangles etc that have exactly the same measures?
They are said to be regular polygons such as equilateral triangles, squares and other polygons that have congruent sides and equal congruent interior angles.
If one of the diagonals of a rhombus is equal to one of its sides find the measures of all the angles?
120,120,60,60
How many ways can you find the sum of measures of the exterior angles of a polygon?
The sum of a regular polygons exterior angles always = 360
Do acute angles have angles whose measures are greater than 90 degrees?
no
How do you find the measures of a rhombus with two diagonals?
That will depend on the lengths of the diagonals of the rhombus which are of different lengths and intersect each other at right angles but knowing the lengths of the diagonals of the rhombus it is then possible to work out its perimeter and area.
How much greater is the sum of the measures of a pair of supplementary angles than the sum of the measures of a pair of copplementary angles?
Complementary angles add up to 90 degrees and supplementary angles add up to 180 degrees. So the answer is 90 degrees greater.
What shape have diagonals that bisect each other at right angles?
Square, rhombus, regular octagon, other regular polygons with 4n sides (where n is an integer).
Do some polygons have a greater number of angles than sides?
No. Because to have an angle you must have adjoining sides.
