Leo+DadMade for Leo
Angles at a Point
Rung 3 of 4 · The traps

Right Picture, Wrong Rule

The maths is easy. The mistake is reaching for 180 when the diagram wanted 360, or subtracting when vertically opposite angles are simply equal. Let's train your eye to pick the right one.


DecideFor each diagram, choose the rule that finds x. Get it wrong and it shows you why.
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All three facts are dead simple on their own. The trap is that the diagrams look similar, so it's easy to grab the wrong rule on autopilot. The fix is to read the picture before you reach for a number.

Trap One — 180 When It Should Be 360 (or the Reverse)

The giveaway is whether the angles sit on a straight edge or fill the whole turn. If you can see a flat line running straight through the point, the angles on one side of it add to 180°. If the angles fan out and there's no straight line splitting them — they go right around — it's 360°. Ask yourself: "is there a straight line here, or a full circle?"

Trap Two — Subtracting When Angles Are Equal

This one stings. When two straight lines cross to make an X and x is the angle directly opposite a known one, the answer is just equal — if the known angle is 70°, then x is 70°. The trap is doing 180 − 70 = 110 out of habit. That 110° is real, but it's the neighbour angle, not the opposite one. Opposite = equal. Next-door = adds to 180.

Say it plainly: straight line through it → 180°. Whole way round → 360°. Directly across an X → equal. Right next door → adds to 180.

Trap Three — Adjacent vs Opposite

In any X-cross there are four angles. Adjacent angles (the two side by side) sit on a straight line, so they add to 180°. Vertically opposite angles (the two facing each other) are equal. Same diagram, two different relationships — so before you write anything, decide which pair you're actually looking at.

Us, Thinking Out Loud

What's the one question you'll ask yourself to decide between 180° and 360°?

In an X-cross, how do you tell the "opposite" angle from the "next-door" one?