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Q: In what polygon have all sides equal length and all angles have equal measure?

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A polygon with sides of equal length and equal angles is termed a regular polygon.

regular

If a shape has equal angles and side lengths then it is known as a regular polygon

Only when it is a regular polygon that all interior angles are of equal measure

regular polygonA square

A regular polygon has equal sides in length and angles.

This is a tautological question that does not have a proper answer. A regular polygon is one which has all its sides of equal length and all its interior angles of equal measure.

a "regular" polygon

All of the angles are equal in a "regular" polygon. (All of the sides are too.)

Only if the polygon is "regular".

If a polygon's sides are all of equal length, it is known as a regular polygon. (The measure of each of its angles will be the same as well)

A regular polygon has all sides of equal length, and all angles of the same measure. An irregular polygon does not fulfil these requirements.

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