Suppose the polygon has V vertices.Then sum of interior angles is (V - 2)*180 degrees = 1980 degrees => V - 2 = 1980/180 = 11 => V = 13 A polygon with V vertices has V*(V-3)/2 = 13*10/2 = 65 diagonals.
It must have 15 sides to comply with the formula:- 0.5*(152-(3*15)) = 90 diagonals So: 360/15 = 24 degrees and 180-24 = 156 degrees Therefore: each interior angle measures 156 degrees
Providing that it is a regular polygon then let its sides be x: So: 0.5*(x2-3x) = 464 diagonals Then: x2-3x-928 = 0 Solving the equation: x = 32 sides Total sum of interior angles: 30*180 = 5400 degrees Each interior angle: (5400+360)/180 = 168.75 degrees
Let its sides be x and use the formula: 0.5*(x squared-3x) = 230 So: x squared-3x-460 = 0 Solving the quadratic equation gives x positive value of 23 Therefore the polygon has 23 sides irrespective of it being a regular or an irregular polygon. Check: 0.5*(23^2-(3*23)) = 230 diagonals
Let its sides be x and rearrange the diagonal formula into a quadratic equation:- So: 0.5(x^2-3x) = 252 Then: x^2-3n-504 = 0 Solving the quadratic equation: gives x a positive value of 24 Therefore the polygon has 24 sides irrespective of it being irregular or regular
1 Let the sides be n and use the formula: 0.5*(n2-3n) = diagonals 2 So: 0.5*(n2-3n) = 170 => which transposes to: n2-3n-340 = 0 3 Solving the above quadratic equation gives n a positive value of 20 4 So the polygon has 20 sides and (20-2)*180 = 3240 interior angles 5 Each interior angle measures: 3240/20 = 162 degrees
Let the number of sides be n and so:- If: 0.5*(n^2 -3n) = 275 Then: n^2 -3n -550 = 0 Solving the above quadratic equation: n has positive value of 25 Each interior angle: (25-2)*180/25 = 165.6 degrees
2520 to get this. You must get the number of sides(16) subtract it by 2, then multiply it by 180. Subtracting it by two is actually the number of triangles inside the polygon showing the possible number of all available non-intersecting diagonals. so in general. The number of non-intersecting triangles multiplied by 180 degrees.( which is the number of degrees in one triangle.
Using the diagonal formula when n is number of sides :- If: 0.5*(n^2-3n) = 189 Then multiplying both sides by 2 and subtracting both sides by 2*189 So: n^2-3n-378 = 0 Solving the above quadratic equation gives n a positive value of 21 Sum of interior angles: (21-2)*180 = 3420 degrees
They begin at the equator, 0 degrees. The end at the poles 90 degrees.
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