An angle is copied without ever knowing how many degrees it is. The compass carries an arc, then carries the distance across that arc, and the new angle is the old one — measured by nobody.
If they get stuck
The answer key prints on a separate page.
Swing an arc from the vertex across both arms, then the same arc from the new ray's endpoint. Set the compass to the gap between the two crossings on the first arc, step that distance round from where the second arc meets the ray, and draw the arm through it. The two triangles you have implicitly built have three equal sides, so the angles at their apexes are equal — SSS, doing the work quietly.
This is the construction that makes the parallel-line construction possible, and it is worth meeting it on its own first. Every angle on these sheets is a whole number of degrees, printed at true size, so a protractor check reads the number the answer key names — even though a protractor is exactly what the construction avoids.
One question off this sheet, worked a step at a time — with a sentence saying what just happened and why.
Copy an angle, step by step