Point z is the incenter of δsrt.

what is mztb?

24°
31°
35°
62°

The line from an incenter to a vertex bisects the angle that is produced there. You probably notice this in angle ASB and angle ARC. Therefore, angle ZTB is going to be equal to half of the angle measure of BTC. We can do the following:

24+24+35+35+x+x=180 (x represents the two angles in angle BTC when they are bisected)
simplifies to
2x+118=180
Solving for x, we get that x=31. 

So angle ZTB=31.

:)