FreeCAD
The easiest way to implement it would simply be to create a reference constraint between one pair, and use it in an expression to create a locking constraint between the other pair. But, of course, that functionality was removed a version or two back, it seems.
Otherwise, it's complicated by two key issues:
1. Four lines have to be selected which form coincidentally-constrained pairs (point-to-point or point-to-object).
2. Control over the constraint must be provided to ensure the correct angles are being matched (i.e., determine which side of the line the angle is applied). This is an issue only if the controlling angle is on a pair of lines which have point-object coincidence (not point-to-point). Otherwise, defaulting to the inside angle where the line endpoints are coincident is probably the best way to go.
That actually leads me to another feature request.
There should be a way, when constraining two lines that intersect each other, which angle should be considered constraining. To that end, I would suggest the following:
1. User selects the lines which are to be constrained
2. User selects the angle constraint
3. User may then:
a. right-click - the angle constraint does what it currently does with no change
b. left click on two end points (one on each line) to determine the angle which is constrained, and the constraint is applied
c. mouse over the two lines and have the UI highlight the angle in the quadrant where the mouse lies. User left-clicks once to apply the constraint to the highlighted angle.
Sorry for the length / complexity of the post (with no pictures). I can try to provide a more visual and detailed explanation of what I'm thinking (in a separate post) , assuming this isn't something that's already been addressed.