Answer:
1 7/10
Step-by-step explanation:
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Segment DF is 1/2 the length of Segment DE. Since the entire segment is DE and it's midpoint is at F, the segment would be broken into 2 equal segments in one. Segment DF and FE. Segment DF is congruent to Segment FE.
Not sure why such an old question is showing up on my feed...
Anyway, let

and

. Then we want to find the exact value of

.
Use the angle difference identity:

and right away we find

. By the Pythagorean theorem, we also find

. (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)
Meanwhile, if

, then (by Pythagorean theorem)

, so

. And from this,

.
So,
7<n<8 is the right answer