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Is a pentagon convex?
A regular pentagon is convex. By taking a regular pentagon and shortening or lengthening one or more sides, an infinite number of possible convex pentagons can be created. A convex polygon is defined as a polygon such that all internal angles are less than or equal to 180 degrees, and a line segment drawn between any two vertices remains inside the polygon. It is possible to have non-convex (concave) pentagons; there are infinite number possible ways to do this, too.
Does there exist a simple graph with 7 vertices having degrees 1 3 3 4 5 6 6?
No. Since the graph is simple, none of the vertices connect to themselves - that is, there are no arcs that loop back on themselves. Then the two vertices with degree 6 must connect to all the other vertices. Therefore there can be no vertex with less than two arcs [ to these two vertices]. So a vertex with degree 1 cannot be part of the graph.
What shape has 3 sides and 2 angles?
No polygon can have less than 3 angles. It would be a triangle with 3 sides but that has 3 angles.
Differentiate convex and non convex polygon?
A convex polygon is one with no angle greater than 180 degrees. A non-convex polygon is one that is not without such an angle.
How many more vertices does a quadrilateral have than a triangle?
zero. 0
