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Q: The sides next to BC are extended to meet at W?
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BC is one side of a regular n-gon the sides next to BC are extended to meet at W Find the measure of angle W in terms of n?

The question is not very coherent. However if the sides either side of BC are able to meet at a point, then the angle between BC and the adjacent sides must be less than 90 degrees. Hence the shape can only be a triangle and since it's regular the angle must be 60 degrees. So if n is 3, the angle (60) is 20n.


Why can't a triangle have parallel sides?

For two sides to be parallel they must not meet at a point (vertex). A triangle has only 3 sides. Let the vertices of a triangle be ABC; then the 3 sides of the triangle are AB, AC and BC. The sides AB and AC meet at vertex A, so they cannot be parallel. The sides AB and BC meet at vertex B, so they cannot be parallel. So Side AB is not parallel to AC (meets at vertex A) and not parallel to BC (meets at vertex B). The only possibility left is that side BC is parallel to side AC. But the sides BC and AC meet at vertex C so they cannot be parallel. Thus none of the sides of a triangle can be parallel.


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