if a regular polygon has n sides, then the number of triangles in that polygon is n - 2. thus, the sum of its interior angles is equal to (n - 2)180°.
because of the formula: (n-2)*180 = total sum of interior angles where n is the number of sides of the polygon.
triangles, rectangles and octagons are all examples of a polygon. a polygon is a polygon whose sides are the same length and whose interior angles are the same measure
20 triangles will fit into a 22 sided polygon whose interior angles add up to 3600 degrees
there r 800 vetices in three triangles
any n-sided polygon (n being any integer) will always have a minimum of n-2 triangles inside the shape, assuming that the polygon is regular with no reflex angles.
this has to do with the way in which the sum of the angles is derived. first you select a point inside the polygon and then join that point to each of the vertices. for a polygon with n sides, this gives rise to n triangles. the sum of the 3 angles of any triangle is 180 degrees. so the sum of the angles of all the triangles is n*180 degrees. now, the "outer" angles of these triangles correspond to the interior angles of the polygon. but the sum also includes the angles formed arounf the central point. the sum of all the angles around this central point is 360 degrees. this is not part of the sum of the interior angles of the polygon and so must be subtracted. thus, the interior angles of a polygon sum to n*180 - 360 degrees or 180*(n- 2) degrees.
540 degrees. you figure it out by seeing how many triangles you can make in the polygon (without crossing lines), and, because triangles equal 180 degrees, you multiply 180 times how many triangles you can make.
by drawing all the diagonals from one vertex, the polygon is divided up into triangles. the sum of the interior angles of the polygon is equal to the sum of the internal angles in the triangles. with n vertices, each vertex is not directly connected to n-3 other vertices, thus n-3 diagonals can be drawn from a vertex which will create n-2 triangles (each with the sum of their interior angles as 180o); so: sum_of_interior_angles = 180 x (number_of_sides - 2)
because the exterior angles of any polygon always add up to 360 degrees
think of the 20 identical triangles that are formed inside the polygon when you draw line segments from the centre of the polygon to each of the polygons corners. the angles of those triangles at the centre of the polygon add to 360 degrees, and there are 20 of them. therefore, each of the angles of the triangles at the centre is 360 / 20 = 18 degrees. the angles within each triangle add to 180 degrees. therefore the other two angles within each triangle, away from the centre of the polygon, add to 180 - 18 = 162 degrees. the two angles are equal. therefore each angle is 162 / 2 = 81 degrees. each interior angle of the 20-sided polygon consists of two of these angles. therefore, the interior angle is 2 x 81 or 162 degrees.
the central angles are the angles of the apexes of the isosceles triangles with the base edges as edges of the polygon and so the central angles make a revolution about the centre of the shape. they will all add to 360. 360/36=10 the polygon with 10 sides is called the decagon.
2700⁰/180⁰ = 15 (triangles)so the polygon has 17 sides.
a polygon is any shape with three straight lines and three angles. shapes such as squares, rectangles, triangles, and pentagons are the most common types of polygons.
yes, they are the same. triangles have 3 sides and 3 angles. squares have 4 sides and 4 angles. octagons have 8 sides and 8 angles.
the total for the interior angles depends on the number of sides. the formula for the total of interior angles of an n-sided polygon is sum =180(n-2). this is 180 degrees for triangles, 360 degrees for quadrilaterals, and 540 degrees for pentagons.
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.
not that i know of, an octagon has eight sides and eight angles. triangles have three of each, as well as hexagons. based on that information, i'm pretty sure it's the same case with any polygon.
this depends on what type of polygon it is.. if it is a regular triangle, then all interior angles measure up to 180 degrees. so, a triangles interior angles would measure 60 degrees each.
it is a triangle. the formula for the total of interior angles in an n-sided polygon is 180(n-2). this is 180 degrees for triangles, 360 degrees for quadrilaterals, and 540 degrees for pentagons.
pick a point around the center of the polygon. join each vertex to this point. you will now have 10 triangles. the total angle of these 10 triangles is 10x180 degrees. now you need to subtract the angles of the ten triangles at the center (which is 360 degrees). therefore total internal angles is (10x180)-360 = 1800-360 which is 1440 degrees. a 10 sided polygon has 20 internal angles. so each angle would be 1440/20 = 144/2 = 72 degrees
they are as follows:- 1 triangles are 2 dimensional polygon shapes 2 triangles have 3 sides 3 triangles may have acute angles greater than 0 but less than 90 degrees 4 triangles may have right angles which are 90 degrees 5 triangles may have obtuse angles greater than 90 but less than 180 degrees 6 triangles have 3 interior angles that add up to 180 degrees 7 triangles have 3 exterior angles that add up to 360 degrees 8 triangles can be scalene which have 3 acute angles 9 triangles can be right angled with a 90 degree angle and 2 acute angles 10 triangles can be obtuse with 1 obtuse angle and 2 acute angles 11 triangles can be isosceles with 2 equal angles and another angle 12 triangles can be equilateral with 3 equal angles of 60 degrees 13 triangles have no diagonals 14 triangles will tessellate 15 triangles have lines of symmetry when they are isosceles or equilateral 16 triangles have perimeters which is the sum of their 3 sides 17 triangles have areas which is 0.5*base*altitude 18 triangles can be used with pythagoras' theorem if they are right angled 19 triangles can be used in conjunction with trigonometry 20 triangles are found in all other polygons 21 triangles and their properties were known by the ancient greeks 22 triangles can be made into musical instruments
similar triangles don't just have proportional angles, they have identical angles!
what is the equation to figure the angles of a polygon?
the sum of the interior angles of a triangle is 180 deg. for a convex polygon with n sides we can divide it to n-2 triangles. so the answer, if the polygon is convex, is (13-2)*180= 1980 deg * * * * * the polygon need not be convex. the formula for the sum of the interior angles is valid as long as the polygon is simple - that it, its sides do not cross each other inside the polygon.
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