If triangle ksd~wat, what is the measure of w? let k=16, d=34 and t=51

You have mentioned that two of the angles of ΔKSD are ∠K=16° and ∠D=34°. So that would mean that ∠S=130°, because∠K+∠D+∠S=180°. That's because all the angles of any triangle must total 180°. But you also say that ∠T=51°. But since no angle of ΔKSD can equal 51°, neither can any angle of ΔWAT equal to 51°. Therefore ∠T=51° is impossible!