Every angle starts from a straight baseline and a pencil mark above it. Put the mark in one spot and you get one angle; move it along and you get a different one. So where would your mark need to go to build an angle of exactly 55°?

You are about to watch three angles being built, one after another. Watch the five moves each time: rule the baseline, place the protractor on the vertex, count up from zero to the size, mark the dot, then join the vertex to the dot. Watch especially the small one — small angles are easy to overshoot.

Now we construct these together: 40°, then 90°, then 135°. Build each one on paper with your protractor — rule the baseline, count up from zero, mark the dot and join the vertex. Then we measure it back on the board tool to prove it is the size we asked for.

Now we work through these together: construct 30°, then 75°, and finally two angles that together make a straight line. Predict where each mark will land before we check it.