By now you know a stack of single angle facts — angles at a point add to 360°, angles on a straight line add to 180°, vertically opposite angles are equal, and all the parallel-line rules. Each one on its own is small. The magic is what happens when you chain them.
One Fact Is Rarely Enough
Real problems hide the angle you want. It's not sitting next to the one you're given — it's two or three steps away. So you hop: use the angle you've got to find a new angle, then use that to find the next, and keep going until you land on the one you were asked for. Each hop is one fact, and that's the chase. In the toy, the marked angle is 62°, but x is right across at the other crossing — you can't get there in one move.
Watch a Chase Unfold
Step one: the angle directly across the X from the 62° one is also 62°, because vertically opposite angles are equal. Step two: slide down the transversal — the matching angle at the bottom crossing is 62° too, by corresponding angles on parallel lines. And x sits on a straight line with that one, so x = 180° − 62° = 118°, by angles on a straight line. Three facts, linked, and the hidden angle falls out.
Why the Reason Matters from Day One
Notice we said why at every hop, not just the number. That's not fussiness — it's the whole skill. A bare number could be a lucky guess; a number with its reason proves you actually reasoned. From the very first chase, get into the habit of saying the fact out loud. It makes the next two rungs easy.