What color throw rugs would you use for sage green Walls and burnt ora

Your best bet is to find one with a neutral beige or grey background that has a pattern with those 2 colours in it. HomeSense/ Home Goods, used to have some with those colours. One had varying shades of those colours in circles, the other squares.

The colours do not have to be an exact match, but should coordinate. I think a solid colour unless sage or orange wouldn't be as effective. The nice thing is, you can use another accent colour from the rug, or incorporate some of the rug's colours in other rooms.

https://www.google.ca/search?q=rugs+with+sage+green+and+burnt+orange&source=lnms&tbm=isch&sa=X&ved=0ahUKEwi26ufC4ZrcAhWhy4MKHb4kAf4Q_AUICigB&biw=1707&bih=844&dpr=1.13

If you want a solid colour maybe achocolate or darker brown would work.