Why not upgrade both your processor and the graphics card? If you're willing to stretch your budget out by $10 to a total of $160, and you're willing to purchase used components; I recommend the following:
Intel Core i3-4150 3.5GHz Dual-Core Processor
($90.00 @ eBay)
XFX Radeon HD 7850 1GB Core Edition Video Card
($70.00 @ eBay)
Prices include shipping, taxes, and discounts when available
The HD 7850 I have selected performs similar to the GTX 295, 480, 570, 650 Ti Boost, 750 Ti and the rebranded R7 265. The HD 7850 supports DX11 and will also provide partial DX12 support via update from AMD. The i3 should also assist in games which utilise Hyper Threading.
All the best.