geometry

A straight angle means the angle is $180^\circ$

Therefore, we can set up the equations to add up to $180^\circ$

$8x-41^\circ+9x+17^\circ=180^\circ$ 

Combining like terms, we get $17x-24^\circ=180^\circ$. We can add $24^\circ$ to each side to get $17x=204^\circ$. Therefore, $x=12^\circ$

Plugging this back into the $m\angle{CBD}$ equation, we get $9x+17^\circ=9(12^\circ)+17^\circ=\boxed{125^\circ}$