Question

To copy an angle using only a compass and a straightedge, begin by marking the vertex of the new angle. Then draw a ray from the vertex, which will be one of the legs of the new angle. What is the next step in the construction?

Answer 1

Set the compass to a convenient width, and draw an arc that is centered at the vertex of the original angle and intersects both legs of the original angle.

Answer 2

The correct answer is:

Place the point of the compass on the vertex of our original angle. Open the compass to a random width and draw an arc through both legs of the angle. Mark the points of intersection with this arc and the sides of the angle.

Explanation:

In order to copy the angle, we need to have some reference for how wide the angle is.

So far all we have is a ray. To get the reference for the width that we need, we will construct an arc in the original angle such that it intersects each side of the angle.

We will then set the compass width to these points of intersection. This will be how we set the width of the new angle.