# Can Point inside quad be determined with angles alone?

### Given

A Quad($C$, $D$, $E$, $B$) and Points $A$, $G$, $F$

### Question

Is it possible by calculating the angles between points to determine whether a point is inside (including on), or outside the quad

### Observations:

Off the top of my head it looks like

$\angle CFB + \angle CFD + \angle DFE + \angle EFB = 360 ^{\circ}$

$\angle CGD = 180 ^{\circ}$ and the other angles: $\angle CGB + \angle BGE + \angle EGD = 180 ^{\circ}$

Is this a valid way to test whether a point lies inside a quad? I can't seem to come up (in my head) with a situation in which the angles from point A would total $360 ^{\circ}$ as well

### Side Note:

I'm hoping to use this information to turn this into a little software routine in python (which it now occurs to me might be subject to rounding errors...)

• ?? typo ∠CGB+∠BGE+∠EGD=180 – oks Dec 24 '14 at 11:03
• fixed... thanks – Jeef Dec 24 '14 at 11:26