Measuring angles with a protractor

An angle has one ray lined up on the `0` mark of a protractor, and the other ray crosses the scale at `65`. Two scales are printed on the protractor: the ray you started from reads `0`, so you count up along that same scale. What is the size of the angle, and is it acute, right, or obtuse?

Art hook Canvas: fix one ray pointing right from the centre; a slider sets the second ray's angle from `0°` to `180°`. Draw the protractor arc behind it and label the live reading. The wedge fills green while acute, gold at exactly `90°`, red when obtuse.

Draw an angle of exactly `140°` with a protractor. Describe your steps, and say what kind of angle it is.

Art hook Interactive: click to place a start point, drag to set the first ray, then type a target angle. The tool snaps a second ray to that exact degree and animates the wedge sweeping open, so drawing `140°` becomes a guided sweep.

Two angles sit side by side on a straight line. One measures `72°`. Without a protractor, work out the other angle. Explain how you know.

Art hook A horizontal line with a pivot dot; drag the shared ray up and down. Two coloured wedges (`72°` and the rest) always fill to the line, and a readout shows both numbers adding to `180°` no matter where you drag.

Four angles meet at a point and go all the way around. Three of them measure `100°`, `85°` and `95°`. What is the fourth angle?

Art hook A spinning pinwheel: place a centre dot and split the full circle into four coloured sectors. Drag the divider lines; the four wedge readings always re-balance to sum to `360°`, like slices of a pie that must fill the whole plate.

A friend measured an angle that clearly looks small and narrow, and wrote down `150°`. What mistake did they probably make, and roughly what should the answer be instead?

Art hook Show one angle with BOTH scale numbers labelled (e.g. `30` and `150`). A toggle lets you pick a scale; if the picked number disagrees with the wedge's acute/obtuse look, the wedge flashes to warn you. Teaches the sanity-check visually.

An angle is right in front of you. One ray sits on `0` and the other crosses the protractor at `30`. What is the angle in degrees?

Art hook Draw a single wedge from a centre dot with a `30°` opening; place a small dot on a circle every `30°` around the centre. Twelve dots appear — one clock face made of equal angles.

Sort these three angle readings into acute or obtuse: `40°`, `95°`, `160°`.

Art hook Three wedges side by side, each auto-coloured: blue for acute, orange for obtuse. Let the viewer add their own wedge with a slider and watch it pick its own colour as it crosses `90°`.

True or false: making the two rays of an angle much longer makes the angle bigger. Explain in one sentence.

Art hook Show the same `40°` wedge three times with rays of different lengths (short, medium, very long). A single label `40°` sits on all three, proving the opening never changes.

Measuring practice: an angle has one ray on `0` and the other crossing at `115`. What is the angle, and is it acute or obtuse?

Art hook Rotate a single ray by `115°` steps around a centre, dropping a dot each time. After several steps a slowly-turning star pattern emerges from the repeated obtuse turn.

Draw an angle of exactly `55°`. List the steps you would follow with a protractor.

Art hook Click-and-type tool: enter `55` and the canvas draws that exact wedge. Stack several copies fanned out from one point to build a hand-drawn-looking fan.

Two angles meet on a straight line. One is `45°`. What is the other one?

Art hook A line with a draggable ray; the two wedges (`45°` and `135°`) are shaded differently and their labels always add to `180°` as you drag.

Three angles meet at a point and go all the way round. Two of them are `130°` and `140°`. What is the third?

Art hook A circle sliced into three sectors from a centre dot; drag two dividers and the third sector's angle updates so all three always total `360°`.

Spot the mistake: Sam lined the protractor's flat edge up but put the centre point a little bit above the vertex, then read `70°`. Why can't we trust that reading, and what should Sam fix?

Art hook An animation showing a protractor with its centre off the vertex giving a wrong wedge, then snapping onto the vertex so the correct wedge locks in — a before/after toggle.

A pizza is cut from the centre into `8` equal slices. What is the angle at the tip of one slice? (Hint: a full turn round the centre is `360°`.)

Art hook Divide a circle into N equal sectors from a slider (`N` from `2` to `12`); each slice shows its tip angle `360°/N`. Colour each slice a rotating hue to make a pie colour wheel.

Reasoning: two angles side by side on a straight line are equal to each other. What must each one measure? Explain.

Art hook A line with a ray that snaps to the exact halfway (perpendicular) position, showing two identical `90°` wedges mirrored across the line — instant line symmetry.

You want to draw a triangle where you turn `120°` at each corner as you walk around it (like a turtle). After the three turns, how much have you turned in total, and why does the path close back into a shape?

Art hook Turtle-on-canvas: walk forward, turn `120°`, repeat three times to close a triangle. Then let a slider change the turn angle and step count — `90°` four times makes a square, `72°` five times a pentagon.

Open-ended: you set two mirror lines through the centre of a kaleidoscope so that `360° ÷ N` sits between them. If you want a `6`-fold flower, what angle should be between the mirrors? What about an `8`-fold star?

Art hook Kaleidoscope canvas: draw a squiggle in one wedge and mirror-repeat it every `360°/N` around the centre. A slider for `N` retunes the angle live, so one doodle blooms into a `6`-fold flower or `8`-fold star.