Seems like I can only work it out if I assume that lineCD is perpendicular to lineAB. I’m not sure I need to know that they’re congruent, so maybe it’s a typo?
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It’s been a long time since I’ve done this, and as I recall they’d mark if angle ADC right, and not let you assume it to be so just because it happens to be drawn so.
For a general solution you could probably use the paw of cosines on triangles ABC and ADC to create two equations for angle CAD in terms of x and y, where y = AD, then solve them. Feels like a rather brutish method though, and I don’t know how pleasant those equations would be, and ugly calculations tend to be a bad sign.
There’s no way that this involves cosines. I’m making of note that it looks like a typo on the answer and solving it that way.
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