Question

Explain how you can use a straightedge and a compass to construct an angle that is both congruent and adjacent to a given angle.

Answer 1

Start with a given angle.

Answer 2

Open the compass and center it at the vertex and draw an arc on each ray of the angle and an extra arc for the other ray we need for the adjacent congruent angle.

Answer 3

Now open the compass from the arc one one ray to the arc on the other ray.
That is open it from points A to B below.