The Descendant is the zodiac sign that was setting on the Western horizon at the moment the chart is calculated for (like a Natal chart). If someone is born around sunset, the Sun will be found close to the Descendant in their chart. In most house systems, it is the cusp of the 7th House of the chart. It is one of the four angles in the chart.
In natal astrology the Descendant sign and 7th house show how you interact with others and the kind of people you tend to be drawn to in close one-to-one connection (like your spouse, business partner or even known enemies).
The Descendant is always opposite the Ascendant in the chart. Some modern astrologers associate the Descendant and 7th house with the zodiac sign Libra.
