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Q: A polygon for which there is a line containing a side of the polygon that also contains a point in the interior of the polygon?

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a convex polygon

Polygon

A point that two sides of a polygon have in common is called a vertex. Each regular polygon has an equal number of sides as vertices.

muh ha ha .....i don't know the point of there even being a one hundred sided shape xxp.s. there isn't even a picture of one!!!!!!

the vertex

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convex

It is concave.

a convex polygon

A convex polygon is defined as a polygon with all its interior angles less than 180°. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Think of it as a 'bulging' polygon. A triangle (3-gon) is always convex.

Then the point is not outside the polygon...?

A rectangular solid is a polygon, as it is a four-sided, six face object. In two dimensions, it will remain a polygon with intersecting lines at the interior, with no line exceeding the boudary of the edge of the object from any point of view.

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.

A point has no interior and so cannot have interior angles.

No. An interior angle is one of many angles in the interior of a closed shape - usually a polygon. The angle sum is the sum of the values of a specified list of angles. They may be angles around a point, angles in one or more shapes.

Polygon

A point and most of the time meets, a polygon is a circle thing that meets at some point!

the point that is equidistant from all vertices of a polygon.

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