[SeoxyS]

(I'm an early-stage angel, fwiw)

Quick counterpoint to the other advice telling you to give more equity out:

1) Your new investors might feel a bit slighted by this; especially if this additional equity is dilutive, which it probably is.

2) A good angel should understand that raising the additional money is in their best interest and will maximize the value of their equity if it helps the company succeed. I'm not sure what situation you're in; but if not being able to raise the extra capital would be a significant risk; then it's a no-brainer.

I would recommend against giving out additional equity. The beauty of convertible debt or safes is that you can take capital whenever you need it without affecting the cap table and it all gets resolved at your first equity round.