You've got the chase and the set-out. Now for the bit that separates a careful mathematician from a careless one: knowing when you're not allowed to use a rule.
Trap One: Assuming Parallel
Co-interior, corresponding and alternate angles only work if the lines are parallel — and the only way you know they're parallel is an arrowhead mark. No arrows? Then the lines might be parallel, might not, and you simply can't use those rules. In the toy, the same two lines appear with and without the marks. With marks, x is findable. Without them, the honest answer is "not enough information" — and saying so is the correct answer, not a cop-out.
Trap Two: Assuming Equal
Same deal with side lengths and angles. Two sides look the same length? Doesn't count unless there are matching tick marks. An angle looks like a right angle? Doesn't count without the little square. The picture is just a sketch; the marks are the facts. Trust the marks, never your eyes.
Trap Three: Thinking There's One "right" Path
Here's the friendlier surprise: when a problem can be solved, there's usually more than one valid chase. You might go co-interior straight to the answer, or corresponding-then-straight-line, and land on the same number. Neither is "more correct". As long as every hop has a reason, any path that gets there earns full marks. So if your route looks different to a friend's, don't panic — check the reasons, not the order.
Every Step Needs Its Justification
Tying it together: a chase is only as strong as its weakest reason. Skip the justification on one hop and the whole argument wobbles. Mark first, fact second, reason written down every single line — that's bullet-proof geometry.