So, the total diagonals will be 6(6-3)/2 = 9. How many sides does this polygon have? The number of diagonals in a polygon that can be drawn from any vertex in a polygon is three less than the number of sides. Ignoring the negative value, n = 6. The formula for the number of vertices in a polygon … D. 1 1. Similarly, substituting (n=5) for a pentagon we get the number of diagonals as 5. Now, we have to find BC = 2 * x.If we draw a perpendicular AO on BC, we will see that the perpendicular bisects BC in BO and OC, as triangles AOB and … Approach: We know that the sum of interior angles of a polygon = (n – 2) * 180 where, n is the number of sides of the polygon. Number of diagonals: 9: The number of distinct diagonals possible from all vertices. In a polygon, it is known that each vertex makes (n-3) diagonals. nC2 - n (where n is the number of sides of the polygon) or in the expanded form: factorial (n) _____ {factorial (2) * factorial (n-2)} substituting (n = 6) for a hexagon we get the number of diagonals as 9. To find the total number of diagonals in a polygon , multiply the number of diagonals per vertex (n - 3) by the number of vertices, n, and divide by 2 (otherwise each diagonal is counted twice). One vertex has three diagonals, so a hexagon would have three diagonals times six vertices, or 18 diagonals. For example, in a hexagon, the total sides are 6. (In general n–2). Hence the polygon has 6 sides (Hexagon). The number of diagonals in a certain regular polygon is equal to five times the number of sides. A regular hexagon has six sides and six vertices. Regular polygons may be either convex or star.In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a … In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). The number of diagonals a polygon has is given by the formula n(n-3)/2. B. In a 20-sided polygon, the total diagonals are = 20(20-3)/2 = 170. C. 1 0. Divide this number by 2 to account for duplicate diagonals between two vertices. (In general ½n(n–3) ). See Diagonals of a Polygon: Number of triangles: 4: The number of triangles created by drawing the diagonals from a given vertex. In this polygon, each vertex makes (20-3) = 17 diagonals. In the figure above, click on "show diagonals" to see them. 8. Draw a regular hexagon and count the maximum number of distinguishable diagonals as shown. 9. But the difficulty is that even in the simplest case which our convex equilateral polygon is a convex regular polygon there are cases which more than one pairs of diagonals share a same point as an intersection and this decreases the total number of intersection points of diagonals. But, since one vertex does not send any diagonals, the diagonals by that vertex needs to be subtracted from the total number of diagonals. So, n(n-3)/2 = 9 given n(n-3) =18 => n^2 - 3n -18 = 0 => n = 6 , -3. The number of diagonals in an n-sided polygon is given by . How many diagonals does a regular hexagon have? Answer: Number of Diagonals = n(n-3)/2. Answer. A. So, sum of interior angles of a hexagon = 4 * 180 = 720 and each interior angle will be 120. A regular hexagon is a polygon with 6 equal sides and equal angles.