Angles as turns

Sort these four angles into the right group — acute, right, obtuse, or reflex: `75°`, `90°`, `160°`, `300°`.

Art hook Draw four dots on a screen; from each, draw two arms opening `75°`, `90°`, `160°`, `300°`. Colour each arm-pair by its type (green=acute, blue=right, orange=obtuse, purple=reflex) so the four families read as a colour-coded row.

Put these angles in order from smallest turn to largest: `210°`, `45°`, `95°`, `180°`, `88°`. Then name the type of each.

Art hook Place a pivot at the screen's left edge and sweep a single rotating arm to each angle in turn, leaving a faint trail. The trails fan out from small to large — a growing peacock tail of turns.

A clock's minute hand starts pointing at 12. It turns clockwise to point at 8, going the LONG way round (12 → 3 → 6 → 8, not the short way). Is the turn acute, right, obtuse, reflex, or a straight angle? Roughly how many degrees? (Each hour-mark is `30°` apart.)

Art hook Build a clock face where clicking a number sweeps the hand from 12 to that number and prints the angle. Colour the swept wedge, and flip the wedge to purple the moment it passes `180°` so 'reflex' becomes a visible tipping point.

Two angles are drawn. The first has very long arms opened just a little. The second has short arms opened very wide. Which is the bigger angle, and why?

Art hook Two pivots side by side, each with a slider for arm length and a slider for opening. Let the viewer stretch the arms and watch the printed degrees NOT change — only the opening slider moves the number.

A right angle is a quarter-turn. How many right angles make a full turn all the way around?

Art hook Rotate a copy of one arm by `90°` four times around a centre dot. The four copies land as a perfect plus-sign / cross — four right angles closing the full turn.

Which of these is a right angle: the corner of a book, a slightly-open pair of scissors, or the two hands of a clock at 6 o'clock?

Art hook Show three angle icons (book corner, scissors, clock at 6). Tapping the right-angle one snaps a little square marker into its vertex and it glows — the classic right-angle tick.

Is each angle acute or obtuse? (a) `30°` (b) `100°` (c) `85°` (d) `179°`

Art hook A dial you can drag from `0°` to `180°`. The wedge is green while under `90°` and turns orange the instant it crosses `90°`, so 'acute' and 'obtuse' are two colours split at the right angle.

Name the type of angle for each turn: a quarter-turn, a half-turn, and a three-quarter-turn.

Art hook One arm pinned at a centre; buttons for ¼, ½, ¾ turn snap it to `90°`, `180°`, `270°` with a smooth animated sweep and a colour-coded trail behind it.

Put these four turns in order from smallest to largest, then name the type of each one: `140°`, `20°`, `90°`, `260°`.

Art hook Draw all four angle-wedges stacked concentrically from the same centre, smallest on top. They nest like the layers of an onion, each turn visibly wider than the last.

Spot the mistake. Sam says: 'This angle has really long arms, so it must be bigger than that one with short arms.' Is Sam right? Explain.

Art hook Take one angle and animate its arms growing longer and shorter on a loop while the printed degree value stays frozen — proof that arm length does not change the angle.

On a clock, the hand turns clockwise from 3 round to 6. How big is that turn, and what type of angle is it? (Hint: each number is `30°` apart.)

Art hook A clock where dragging the hand between hours shows the running degree count in steps of `30°`. Sweep from 3 to 6 and a right-angle square pops into the corner when it hits `90°`.

True or false, and fix it if false: 'A reflex angle is any angle bigger than a right angle.'

Art hook A `0°`–`360°` dial with two markers at `90°` and `180°`. As you sweep, a label reads acute → right → obtuse → straight → reflex, changing exactly at those two lines.

A robot facing north turns clockwise a quarter-turn, then another quarter-turn, then another. Which way is it facing now, and what total angle has it turned through?

Art hook A little arrow-robot on screen. Each 'turn' button rotates it `90°` clockwise with a swept arc showing the cumulative angle. After three presses the arc is a `270°` reflex fan and the robot points west.

Design challenge: choose four different angles so that you have exactly one acute, one right, one obtuse, and one reflex angle. Write your four sizes and label each.

Art hook A make-your-own gallery: four pivots where the viewer dials each angle. The canvas only 'accepts' the set once it detects one of each type — a tiny puzzle that rewards a full acute/right/obtuse/reflex collection with a celebratory bloom.

You want to place `6` identical petals evenly all the way around a centre point. What turn (in degrees) should there be between one petal and the next?

Art hook Directly the dot-multiplier idea: draw one petal, then rotate copies by `60°` six times around a centre. The result is a six-petal flower — the `60°` gap between arms is the whole design.

Two angles share the same pair of arms. One of them measures `110°`. Without a protractor, what is the size of the reflex angle on the other side, and how do you know?

Art hook Draw both angles round one shared pair of arms in two colours — one wedge `110°`, the other `250°`. Together they fill the whole circle, showing the two turns adding to `360°`.