Problem list（18 problems）
- How many degrees is angle x? The angles of a triangle add to 180° because cutting them off and lining them up makes a straight line
- How many degrees is angle x? "Vertically opposite angles are equal" is not a rule to memorise — you can rebuild it from "a straight line is 180°"
- How many degrees is angle x? "Exterior angle = sum of the two non-adjacent interior angles
- Sum of the interior angles of a hexagon? The formula is 180 × (corners − 2)
- How many degrees is angle x? "Equal sides mean equal angles
- How many degrees is angle x? Any zigzag between parallel lines yields to one move: draw a parallel line through the bend
- How many degrees is angle x? The dented vertex equals the sum of the other three angles
- What is A＋B＋C＋D＋E? Nowhere does this argument use "because it is regular"
- How big is angle x? Repeat one move and the numbers line up
- How many degrees is angle x? Every folding problem runs on two facts: overlapping angles are equal, and the strip's parallel edges give equal alternate angles
- How big is angle BIC? You never learn B and C separately — but knowing their sum is enough to know the sum of their halves
- How many degrees is angle x? A regular pentagon is built out of just 108° and 36°
- How many degrees is angle x? When a triangle appears inside a circle, hunt for "all radii are equal" first
- How big is angle AED? Whenever a square meets an equilateral triangle, start from the 30° left over between 90° and 60°
- How many degrees is the gap angle x? Equilateral triangles, squares and regular hexagons tile the plane; regular pentagons cannot — 108° does not divide 360° exactly
- At 3:40, what angle do the hands make? Six degrees a minute for the minute hand, half a degree for the hour hand
- Through what angle must it turn to match itself again? The turn that brings a shape back onto itself is "a full turn ÷ the number of corners"
- What is the angle at the centre of the sector? The whole of a cone's net rests on one fact: arc = base circumference
Other ideas
- Shearing — moving a shape without changing its area
- Ratios — answers without fixing a single number
- Add, then subtract — an overlap is a counting problem
- Circles and sectors — multiply by π once, at the very end
- Decide how to count, then count
- Flatten the solid before you think about it
- Write the same thing two different ways
- Fold it, turn it, copy it across
- Back to why the formula works