Angle between two lines

If I have two curves (say x^2 and 1-x^2) and I want to find the angle between them at the points of their interception, how would I go about doing it?

I have equated both and found their points of interception, and differentiated them both to find the gradient at the points of interception. And I know that the gradient is = tan theta, where theta is the angle between the tangent to the curve at that point and the x-axis.
But now Im not sure how to go about finding thr angle *between* the curves?? Is it just the angle between the two tangent lines at that point of interception?

if you imagine the two tangents making a letter X, the angle you need is the angle between the branches of the X. so if one tangent angle was 82°
and the other was 59° from the horizontal then the angle between is 23°

WHy would you subtract and not add? because if the angles are both towards the horizontal

if two arrows are sticking into the same point on the ground: one is at 80 degrees to the ground, the other at 50 degrees to the ground... the angle between the arrows is 30 degrees.

but how do you know its the angle from that direction? couldnt it be the angle from the opposite horizontal direction?

Find the gradients and find angles by using trigonometry. Really it's easiest to draw diagrams.

typically you use the direction going to the right from the origin as your basis.

im just confused about which angle im actually finding tbh