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Euclid parallel postulate can be interpreted as being equivalent to the sum of the angles of a [plane] triangle being 180 degrees.

It is quite easy to prove that a polygon with n sides can be divided into n triangles. Putting the two together, you get the formula for the sum of the interior angles of a polygon.

Q: Where does the formula for the sum of interior angles of a polygon come from?

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No. A square has to have 4 equal sides with interior angles of exactally 90 degrees. A rhombus has to have 4 equal sides only. (any angles (although to be the same length the angles come in pairs).)

Construct a 144° angle with two equally long lines. Keep on adding sides until you come back to the beginning. Count the sides. Mathematicaly you could divide a full circle with the value of the difference between the interior angel and a straight line (180°) So: 360° / (180° - 144° ) = 10 You will in either case get decagon (ten sided figure)

A set square is a tool for marking angles in engineering and technical drawing, etc. They come in different angles and may be adjustable.

It can, but it doesn't have to. The base can be any polygon, as long as the sides are triangles that come to a point at the top.

from a pyramid

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A decagon is a ten-sided figure.If each angle is equal, then each angle is 144,000 degrees. To find the degrees in any figure, take the sides of a figure (1000) minus 25213249 times 180. (10145888774-2458)180 equals 1440. * * * * * Looks like the original answer got garbled. To find the sum of the interior angles of any polygon, take the [sides of a figure (10) minus 2] times 180. (10 - 2)*180 equals 1440.

n=number of sides s=sum of interior angles s=180(n-2)

The name of a triangle came from the number of angles it has, 'tri' meaning three.

(The exterior angles of a regular polygon total 360 degrees. 360 divided by 40 = 9 sides. For a more difficult way to come up with the same information, read on.)Okay, this is probably not the most efficient or simple way to do the problem, but I'll show you the way I did it.First you determine the measure of the interior angles that correspond with the exterior angles. The exterior and interior angles form a straight line. Since a straight line is always 180 degrees:40+y=180where y= the measure of any interior angle (they're all the same)40+y-40=180-40y=140so, the interior angles are 140 degreesThen I wrote a formula to find the total measure of the interior angles of a regular polygon given n sides.A regular triangle has 180 total degrees, a square has 360, a pentagon has 540, etc.A formula that works for all of these is:x=180(n-2)where n is the number of sides andwhere x is the total measure of the interior anglesTo get the measure of each angle you simply divide by n, so we now have:x/n=180*(n-2)/nI'll replace the x/n with y for simplicity(y=the measure of each interior angle)y=180*(n-2)/nNow simplify the equation to simplest termsy=180*(n-2)/ny=180*((n/n)-(2/n))y=180*(1-(2/n))y=180-(360/n) (Distributive property)We have already figured out y from earlier in the problem, so just plug it in and solve for n.140=180-(360/n)-40=-360/n40=360/nn(40)=(360/n)n40n=360n=9

No. A square has to have 4 equal sides with interior angles of exactally 90 degrees. A rhombus has to have 4 equal sides only. (any angles (although to be the same length the angles come in pairs).)

In a tessellation a number of polygons meet at a point. If n polygons meet, then there will be n vertices. These must add up to 360 degrees so that the tessellation does not leave holes. So the interior angles of the polygon must be a factor of 360 degrees. Interior angle of an equilateral triangle = 60 deg = 360/6 and so it will tessellate; Interior angle of a square = 90 deg = 360/4 and so it will tessellate; Interior angle of a regular pentagon = 108 deg which is not a factor of 360 and so it will not tessellate; etc.

Construct a 144° angle with two equally long lines. Keep on adding sides until you come back to the beginning. Count the sides. Mathematicaly you could divide a full circle with the value of the difference between the interior angel and a straight line (180°) So: 360° / (180° - 144° ) = 10 You will in either case get decagon (ten sided figure)

NOA polygon is a closed, 2-dimensional (planar) shape made up of three or more straight line segments connected end to end to end.By this definition, triangles, quadrilaterals and pentagons are all examples of polygons. Circles (etc.) are not, as they are not composed of (straight) line segments. Note that the shape can be convex (which we're used to) or concave, meaning that all the straight line segments may not lie along a "perimeter" but can "go inside" and "come back out" to form the shape.:(For illustrations, see related link)Regular versus Irregular PolygonsThe sides of a regular polygon are all equal. Also, the internal angles are equal to each other, whereas an irregular polygon's interior angles are unequal. Think of a Stop sign. That is a regular octagon. Any distortion of it -- changing the length of one side or increasing (decreasing) any of the angles would result in an irregular octagon. A regular polygon is a convex plane shape with all of its sides the same length, and all its internal angles the same size. An irregular polygon will have unequal sides and angles, and can be either convex or concave. For example, regular polygons are equilateral triangles and squares, irregular polygons include 'scalene triangles', rhombi (angles differ), and rectangles (2 sides longer).In a regular polygon, all the sides are congruent to each other. All the angles are congruent to each other. A regular triangle (also known as an equilateral triangle) has all of its sides measuring the same length and all three of its interior angles measure 60 degrees. So it is equilateral and equiangular.A polygon with n sides is termed as regular only when each of its angles is given by (n-2)/n*180 and the ratio between any two sides is 1:1.Examples of Regular PolygonsEquilateral triangleSquareExamples of Irregular PolygonScalene triangleRectangle ("oblong")Convex PolygonA convex polygon is a 3 or more sided shape where any straight, non-tangent line would intersect only two sides and only two points. A concave polygon has sides that, if extended as lines, would intersect a non-adjacent side. (see examples at related link)

The word "hexagon" comes from Greek, with "hexa" meaning "six" and "gonia" meaning "angle." It refers to a polygon with six sides and six angles.

No, a ray is a straight line with no ending points. And a polygon has lines that come together at points.

The ancient Greeks because polygon come from a Greek word meaning 'many sides'

In order for a polygon to tessellate, the angles must add up to 360 degrees, to come full circle. Triangles have 60 degree angles, so 6 of them circle together. Squares have 90 degree angles, so 4 of them tessellate to a point. Hexagons can even tessellate, because the 120 degree angles add up to 360. But pentagons have 108 degree angles. Three of them add up to 324, only leaving 36 degrees left to close the circle.