Virtual protractor and angle maker

What the angle maker shows

An angle measures the amount of turn between two arms that meet at a point called the vertex. On this page a protractor sits under the arms. Drag the handle and the angle opens from 0° up to a full turn of 360°, snapping to whole degrees, or to 5° steps if you turn that option on. The readout gives the size and the type.

• Acute: more than 0° and less than 90°.
• Right: exactly 90°, a quarter turn.
• Obtuse: more than 90° and less than 180°.
• Straight: exactly 180°, a half turn.
• Reflex: more than 180° and less than 360°.
• Full turn: 360°.

Why turning helps

Children often meet angles as still pictures, but an angle is really a turn. Common Core standard 4.MD.C.5 describes angles this way: a one-degree angle turns through 1/360 of a circle. Dragging the handle all the way round makes that literal. Hide the number adds estimation, which builds a feel for benchmark angles like 45°, 90°, 180° and 270°, so a child can tell when a measured answer cannot be right.

Common mix-ups

• Thinking longer arms make a bigger angle. The size depends only on the turn. Have a child sketch two 40° angles on paper, one with short arms and one with long arms, and compare.
• Reading the wrong scale. Paper protractors have two scales, so a child measuring an obtuse angle may read 50° instead of 130°. Estimating first catches this, because an obtuse angle cannot be 50°.
• Only recognizing upright right angles. A right angle is still 90° when it is tilted, so point out right angles at different slants around the room.
• Struggling with reflex angles. A half-circle protractor stops at 180°, so measure the smaller angle and subtract it from 360°. Here, making 300° and noticing that 60° is left over shows why.

A 10-minute angle session

• Turn on Hide the number. Ask for a right angle, let the child drag, then reveal.
• Repeat for 45°, 180° and 270°, talking about each as a fraction of a turn.
• Switch on Challenge. Before each target, the child names the type it will be.
• Make 120° and ask how far it is to 180° and to 360°. Drag on to check: 60° and 240°.
• End by asking the child to describe in their own words how they estimate an angle.

Where it fits by grade

• Grade 4: understand degrees (4.MD.C.5), measure and sketch angles in whole degrees (4.MD.C.6), add angles together (4.MD.C.7), and identify right, acute and obtuse angles (4.G.A.1).
• Grade 7: supplementary, complementary, vertical and adjacent angles (7.G.B.5).
• Grade 8: angle sums and exterior angles of triangles (8.G.A.5).
• England: Year 3 introduces right angles and turns, Year 4 covers acute and obtuse angles, and Year 5 measures in degrees, including reflex angles, angles on a straight line (180°) and around a point (360°). Year 6 and Key Stage 3 build on these angle facts.

Learning more

Angles are a skill on Eurekami's skill map, and lessons draw diagrams live from the numbers in each question. Daily Practice brings angle facts back when they start to fade, and when a geometry question is tricky the AI tutor asks guiding questions so the student does the reasoning.