Why the usual answer is so thin
The sign is the coarsest fact in a chart. It groups everyone born inside a month long window and says nothing that separates one of them from another. On a date like this one, where no boundary is anywhere near, naming the sign takes a sentence and leaves nothing further to add.
The degree does the opposite. It narrows the Sun to a strip a day wide, it is computable from a year and a birthplace, and it feeds directly into the parts of a chart that actually vary: aspects to other planets, the house the Sun occupies, and which face of the sign applies.
None of which makes the sign wrong. It is simply the first line of an answer that most pages treat as the whole of it, and the parts left out are the parts that would tell one 7 June birth from another.
Sixteen degrees, and what sits there
Sixteen degrees is in the upper half of Gemini's second face, the band from ten to twenty. The Chaldean order hands that face to Mars. The triplicity scheme reads it as the Libra portion of Gemini and gives it to Venus instead, so the two readings pull in noticeably different directions.
That disagreement is worth naming rather than hiding. It is not evidence that one table is wrong; the schemes were built for different purposes and both survived. What matters in practice is that a page quoting a decan ruler should say which order it is drawing on.
A figure that holds across generations
Someone born on 7 June in 1938 and someone born on the same date in 2030 have their Suns within about a degree and a half of one another. The calendar and the orbit are kept in step by the leap year cycle, which returns the date to nearly the same point each time.
That stability is why a printed table can get the sign right for a whole century without being updated. It is also why the same table fails badly at the two edges of a sign, where a degree and a half is enough to cross a boundary and change the answer.
The wobble itself is a sawtooth rather than a slope. Positions creep forward across three ordinary years and then fall back when February gains a day, so the same date returns to almost the same place on a four year rhythm rather than wandering steadily in one direction.
The parts a date cannot supply
The Moon travels roughly its own diameter every hour and a whole sign in about two and a half days, so a 7 June birth can land it in one of two signs, and the hour decides which. Nothing on the calendar page will tell you.
The ascendant is worse still for anyone working from a date alone: it turns through all twelve signs in a day and depends on latitude as well as time. The widget above takes a year, a time and a place, returns the exact solar degree, and reports the margin to the nearest boundary.
Houses depend on the same information. They divide the chart relative to the horizon and the meridian, so without an hour the Sun has a degree and a sign but no house, and the aspects it makes to the Moon and the angles cannot be listed either.
Questions people ask about this
What sign is 7 June?
Gemini, without qualification. The date sits well inside the sign, so no birth year, hour or time zone produces a different answer.
How many degrees into Gemini is this date?
Roughly sixteen. Across 1930 to 2035 the noon figure ranged from about fifteen point eight to seventeen point two degrees.
Why do birthday pages all sound alike?
Because most of them work from the sign alone, and the sign is identical for everyone born across a month. Once the degree and the face are included, one Gemini birthday reads differently from the next.
Which face of Gemini is sixteen degrees in?
The second, ten to twenty degrees. Mars holds it in the Chaldean sequence and Venus by way of Libra in the triplicity count.
Do I need a birth time for this date?
Not for the sun sign, which is settled either way. You need it for the Moon, the rising sign and the houses, and for the exact degree rather than an approximate one.
Is this birthday close to Cancer?
Not particularly. About fourteen degrees of Gemini remain after this point, which is roughly a fortnight of calendar time before the solstice crossing.