How do I turn off these valves?

[Justmarcey]

I'm trying to shut off the sink so I can fix the leaky faucet.... but these valves on this particular sink are different than all the others in my house. Picture 1 looks like you'd turn it 90 and it would shut off, however it just spins in circle. So I thought maybe it was a push pull but as you can see from photo 2 it just pops off and looks broken on the inside. Photo 3 shows it without the weird broken cap. How in the world do I shut this thing off? Any help and guidance is greatly appreciated.

 

[Twowaxhack]

The one handle is cracked. The stems are probably frozen up. If you turn them, there’s a chance they’ll start dripping from the stem.

The repair for that is to replace the valves.

You could turn the brass stem 90 degrees to the right and that may cut the water off. Keep in mind if you turn it and it starts dripping, replacement will most likely be required.