Answer
The angle with a tangent of $1$ would be an angle that measures $45^{\circ}$. This is logical because the tangent ratio is $\frac{opposite}{adjacent}$. In a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle, the two legs (which correspond to opposite and adjacent sides of each of the angles, not including the right angle) would be congruent, so the ratio of their lengths is $1$.
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