An angle can be constructed as a copy of a given angle using a compass. To begin, place the sharp end of the compass at the vertex of the angle. Then, draw an arc across the rays any distance from the vertex.
Next, sketch an approximation of one of the rays — here that is the horizontal ray. Without changing the settings of the compass, position the sharp end at the endpoint of the copied ray, and draw an arc.
Next, adjust the compass to measure the distance between the rays at their points of intersection with the arc on the original angle. Keeping this measurement, align the sharp point with the arc's point of intersection with the horizontal ray on the copy. Mark this distance on the other end of the arc.
On the copy, the second ray can be drawn from the endpoint on the first ray. Draw a segment from this point through the marked position on the arc.