2D line intersection given 2 points (line) and a point with angle

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Given $2$ points (limited length), and a point with angle(unlimited). How do I check if they will intersect or not?

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I've only been able to find line-line or $4$ points intersections.

Current progress :

line-angle: $y-x = \cot(d) * (x-mx)$
point-point: $(y-b)(c-a) = (x-a)(d-b)$ # sorry the d here is from (c,d), not the angle

How can I merge these together? Thank you