The points $\displaystyle {A}$, $\displaystyle {B}$, $\displaystyle {C}$, $\displaystyle {X}$ are colinear (and occur as sequentially given). The point $\displaystyle {T}$ is on the perpendicular of $\displaystyle \overline{{{A}{X}}}$ passing through the point $\displaystyle {X}$. The distance from $\displaystyle {A}$ to $\displaystyle {B}$ is 2-in. The distance from $\displaystyle {B}$ to $\displaystyle {C}$ is the same. The distance from $\displaystyle {C}$ to $\displaystyle {X}$ is 14-in. Finally, the distance from $\displaystyle {T}$ to $\displaystyle {X}$ is 12. For convenience, let $\displaystyle \alpha=\angle{T}{A}{X}$, $\displaystyle \beta=\angle{T}{B}{X}$, and $\displaystyle \gamma=\angle{T}{C}{X}$.

First, draw a clearly labeled picture of this scenario.

Second, find the exact value of $\displaystyle {\tan{{\left(\alpha+\beta+\gamma\right)}}}=$ Preview Question 6 Part 1 of 2   .

Third, and finally, find $\displaystyle \alpha+\beta+\gamma=$ °